Chapter 4 Resource Masters - Morgan Park High School
Transcript of Chapter 4 Resource Masters - Morgan Park High School
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.
Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7
ANSWERS FOR WORKBOOKS The answers for Chapter 4 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-827728-0 Algebra 1Chapter 4 Resource Masters
2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03
Glencoe/McGraw-Hill
© Glencoe/McGraw-Hill iii Glencoe Algebra 1
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 4-1Study Guide and Intervention . . . . . . . . 213–214Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 215Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 216Reading to Learn Mathematics . . . . . . . . . . 217Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 218
Lesson 4-2Study Guide and Intervention . . . . . . . . 219–220Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 221Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 222Reading to Learn Mathematics . . . . . . . . . . 223Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 224
Lesson 4-3Study Guide and Intervention . . . . . . . . 225–226Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 227Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Reading to Learn Mathematics . . . . . . . . . . 229Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 230
Lesson 4-4Study Guide and Intervention . . . . . . . . 231–232Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 233Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Reading to Learn Mathematics . . . . . . . . . . 235Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 236
Lesson 4-5Study Guide and Intervention . . . . . . . . 237–238Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 239Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 240Reading to Learn Mathematics . . . . . . . . . . 241Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 242
Lesson 4-6Study Guide and Intervention . . . . . . . . 243–244Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 245Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 246Reading to Learn Mathematics . . . . . . . . . . 247Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 248
Lesson 4-7Study Guide and Intervention . . . . . . . . 249–250Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 251Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 252Reading to Learn Mathematics . . . . . . . . . . 253Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 254
Lesson 4-8Study Guide and Intervention . . . . . . . . 255–256Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 257Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 258Reading to Learn Mathematics . . . . . . . . . . 259Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 260
Chapter 4 AssessmentChapter 4 Test, Form 1 . . . . . . . . . . . . 261–262Chapter 4 Test, Form 2A . . . . . . . . . . . 263–264Chapter 4 Test, Form 2B . . . . . . . . . . . 265–266Chapter 4 Test, Form 2C . . . . . . . . . . . 267–268Chapter 4 Test, Form 2D . . . . . . . . . . . 269–270Chapter 4 Test, Form 3 . . . . . . . . . . . . 271–272Chapter 4 Open-Ended Assessment . . . . . . 273Chapter 4 Vocabulary Test/Review . . . . . . . 274Chapter 4 Quizzes 1 & 2 . . . . . . . . . . . . . . . 275Chapter 4 Quizzes 3 & 4 . . . . . . . . . . . . . . . 276Chapter 4 Mid-Chapter Test . . . . . . . . . . . . 277Chapter 4 Cumulative Review . . . . . . . . . . . 278Chapter 4 Standardized Test Practice . . 279–280
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A35
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 4 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 4 Resource Masters includes the core materials neededfor Chapter 4. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 4-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 4Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 252–253. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
44
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 4.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
arithmetic sequence
axes
common difference
coordinate plane
koh·AWRD·nuht
dilation
dy·LA·shuhn
function
image
inductive reasoning
ihn·DUHK·tihv
inverse
linear equation
mapping
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
origin
quadrant
KWAH·druhnt
reflection
rotation
sequence
standard form
terms
transformation
translation
vertical line test
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
44
Study Guide and InterventionThe Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-14-1
© Glencoe/McGraw-Hill 213 Glencoe Algebra 1
Less
on
4-1
Identify Points In the diagram at the right, points are located in reference to two perpendicular number lines called axes. The horizontal number line is the x-axis, and the verticalnumber line is the y-axis. The plane containing the x- and y-axes is called the coordinate plane. Points in the coordinate plane arenamed by ordered pairs of the form (x, y). The first number, or x-coordinate corresponds to a number on the x-axis. The secondnumber, or y-coordinate, corresponds to a number on the y-axis.
The axes divide the coordinate plane into Quadrants I, II, III,and IV, as shown. The point where the axes intersect is called the origin. The origin has coordinates (0, 0).
x
y
O
PQ
R
Quadrant III
Quadrant II Quadrant I
Quadrant IV
Write an orderedpair for point R above.
The x-coordinate is 0 and the y-coordinate is 4. Thus the orderedpair for R is (0, 4).
Write ordered pairs for pointsP and Q above. Then name the quadrant inwhich each point is located.
The x-coordinate of P is �3 and the y-coordinate is�2. Thus the ordered pair for P is (�3, �2). P is inQuadrant III.
The x-coordinate of Q is 4 and the y-coordinate is�1. Thus the ordered pair for Q is (4, �1). Q is inQuadrant IV.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Write the ordered pair for each point shown at the right. Name the quadrant in which the point is located.
1. N 2. P
3. Q 4. R
5. S 6. T
7. U 8. V
9. W 10. Z
11. A 12. B
13. Write the ordered pair that describes a point 4 units down from and 3 units to the rightof the origin.
14. Write the ordered pair that is 8 units to the left of the origin and lies on the x-axis.
x
y
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P
QR
N
S
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V
W
Z
AB
© Glencoe/McGraw-Hill 214 Glencoe Algebra 1
Graph Points To graph an ordered pair means to draw a dot at the point on thecoordinate plane that corresponds to the ordered pair. To graph an ordered pair (x, y), beginat the origin. Move left or right x units. From there, move up or down y units. Draw a dot atthat point.
Plot each point on a coordinate plane.
a. R(�3, 2)Start at the origin. Move left 3 units since the x-coordinate is �3. Move up 2 units since the y-coordinate is 2. Draw a dot and label it R.
b. S(0, �3)Start at the origin. Since the x-coordinate is 0, the point will be located on the y-axis. Move down 3 units since the y-coordinate is �3. Draw a dot and label it S.
Plot each point on the coordinate plane at the right.
1. A(2, 4) 2. B(0, �3)
3. C(�4, �4) 4. D(�2, 0)
5. E(1, �4) 6. F(0, 0)
7. G(5, 0) 8. H(�3, 4)
9. I(4, �5) 10. J(�2, �2)
11. K(2, �1) 12. L(�1, �2)
13. M(0, 3) 14. N(5, �3)
15. P(4, 5) 16. Q(�5, 2)
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Study Guide and Intervention (continued)
The Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-14-1
ExampleExample
ExercisesExercises
Skills PracticeThe Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-14-1
© Glencoe/McGraw-Hill 215 Glencoe Algebra 1
Less
on
4-1
Write the ordered pair for each point shown at the right.Name the quadrant in which the point is located.
1. A 2. B
3. C 4. D
5. E 6. F
Write the ordered pair for each point shown at the right.Name the quadrant in which the point is located.
7. G 8. H
9. J 10. K
11. L 12. M
Plot each point on the coordinate plane at the right.
13. M(2, 4) 14. N(�3, �3)
15. P(2, �2) 16. Q(0, 3)
17. R(4, 1) 18. S(�4, 1)
Plot each point on the coordinate plane at the right.
19. T(4, 0) 20. U(�3, 2)
21. W(�2, �3) 22. X(2, 2)
23. Y(�3, �2) 24. Z(3, �3)W
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A
© Glencoe/McGraw-Hill 216 Glencoe Algebra 1
Write the ordered pair for each point shown at the right. Name the quadrant in which the point is located.
1. A 2. B
3. C 4. D
5. E 6. F
7. G 8. H
9. I 10. J
11. K 12. L
Plot each point on the coordinate plane at the right.
13. M(�3, 3) 14. N(3, �2) 15. P(5, 1)
16. Q(�4, �3) 17. R(0, 5) 18. S(�1, �2)
19. T(�5, 1) 20. V(1, �5) 21. W(2, 0)
22. X(�2, �4) 23. Y(4, 4) 24. Z(�1, 2)
25. CHESS Letters and numbers are used to show the positions of chess pieces and to describe their moves.For example, in the diagram at the right, a white pawn is located at f5. Name the positions of each of theremaining chess pieces.
ARCHAEOLOGY For Exercises 26 and 27, use the grid at the right that shows the location of arrowheads excavated at a midden—a place where people in the past dumped trash, food remains, and other discarded items.
26. Write the coordinates of each arrowhead.
27. Suppose an archaeologist discovers two other arrowheads located at (1, 2) and (3, 3). Draw an arrowhead at each of these locations on the grid.
0 1 2Meters
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a b c d e f g h
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Practice The Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-14-1
Reading to Learn MathematicsThe Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-14-1
© Glencoe/McGraw-Hill 217 Glencoe Algebra 1
Less
on
4-1
Pre-Activity How do archaeologists use coordinate systems?
Read the introduction to Lesson 4-1 at the top of page 192 in your textbook.
What do the terms grid system, grid, and coordinate system mean to you?
Reading the Lesson
1. Use the coordinate plane shown at the right.
a. Label the origin O.
b. Label the y-axis y.
c. Label the x-axis x.
2. Explain why the coordinates of the origin are (0, 0).
3. Use the ordered pair (�2, 3).
a. Explain how to identify the x- and y-coordinates.
b. Name the x- and y-coordinates.
c. Describe the steps you would use to locate the point for (�2, 3) on the coordinateplane.
4. What does the term quadrant mean?
Helping You Remember
5. Explain how the way the axes are labeled on the coordinate plane can help youremember how to plot the point for an ordered pair.
© Glencoe/McGraw-Hill 218 Glencoe Algebra 1
MidpointThe midpoint of a line segment is the point that lies exactly halfwaybetween the two endpoints of the segment. The coordinates of themidpoint of a line segment whose endpoints are (x1, y1) and (x2, y2)
are given by � , �.
Find the midpoint of each line segment with the given endpoints.
1. (7, 1) and (�3, 1) 2. (5, �2) and (9, �8)
3. (�4, 4) and (4, �4) 4. (�3, �6) and (�10, �15)
Plot each segment in the coordinate plane. Then find the coordinates of themidpoint.
5. J�K� with J(5, 2) and K(�2, �4) 6. P�Q� with P(�1, 4) and Q(3, �1)
You are given the coordinates of one endpoint of a line segment and the midpoint M. Find the coordinates of the other endpoint.
7. A(�10, 3) and M(�6, 7) 8. D(�1, 4) and M(3, �6)
(3, –1)
(–1, 4)
(1, 1.5)
x
y
O
P
Q
(5, 2)
(–2, –4)
(1.5, –1)x
y
O
K
J
y1 � y2�2
x1 � x2�2
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
4-14-1
Study Guide and InterventionTransformations on the Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-24-2
© Glencoe/McGraw-Hill 219 Glencoe Algebra 1
Less
on
4-2
Transform Figures Transformations are movements of geometric figures. Thepreimage is the position of the figure before the transformation, and the image is theposition of the figure after the transformation.
Reflection A figure is flipped over a line.
Translation A figure is slid horizontally, vertically, or both.
Dilation A figure is enlarged or reduced.
Rotation A figure is turned around a point.
Determine whether each transformation is a reflection, translation,dilation, or rotation.
a. The figure has been flipped over a line, so this is a reflection.
b. The figure has been turned around a point, so this is a rotation.
c. The figure has been reduced in size, so this is a dilation.
d. The figure has been shifted horizontally to the right, so this is atranslation.
Determine whether each transformation is a reflection, translation, dilation, orrotation.
1. 2.
3. 4.
5. 6.
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 220 Glencoe Algebra 1
Transform Figures on the Coordinate Plane You can perform transformationson a coordinate plane by changing the coordinates of each vertex. The vertices of the imageof the transformed figure are indicated by the symbol �, which is read prime.
Reflection over x-axis (x, y ) → (x, �y )
Reflection over y-axis (x, y ) → (�x, y )
Translation (x, y ) → (x � a, y � b)
Dilation (x, y ) → (kx, ky )
Rotation 90� counterclockwise (x, y ) → (�y, x )
Rotation 180� (x, y ) → (�x, �y )
A triangle has vertices A(�1, 1), B(2, 4), and C(3, 0). Find thecoordinates of the vertices of each image below.
Study Guide and Intervention (continued)
Transformations on the Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-24-2
ExampleExample
a. reflection over the x-axisTo reflect a point over the x-axis,multiply the y-coordinate by �1.
A(�1, 1) → A�(�1, �1)B(2, 4) → B�(2, �4)C(3, 0) → C�(3, 0)
The coordinates of the image vertices areA�(�1, �1), B�(2, �4), and C�(3, 0).
b. dilation with a scale factor of 2Find the coordinates of the dilated figureby multiplying the coordinates by 2.
A(�1, 1) → A�(�2, 2)B(2, 4) → B�(4, 8)C(3, 0) → C�(6, 0)
The coordinates of the image vertices areA�(�2, 2), B�(4, 8), and C�(6, 0).
ExercisesExercises
Find the coordinates of the vertices of each figure after the given transformationis performed.
1. triangle RST with R(�2, 4), S(2, 0), T(�1, �1) reflected over the y-axis
2. triangle ABC with A(0, 0), B(2, 4), C(3, 0) rotated about the origin 180°
3. parallelogram ABCD with A(�3, 0), B(�2, 3), C(3, 3), D(2, 0) translated 3 units down
4. quadrilateral RSTU with R(�2, 2), S(2, 4), T(4, 4), U(4, 0) dilated by a factor of
5. triangle ABC with A(�4, 0), B(�2, 3), C(0, 0) rotated counterclockwise 90°
6. hexagon ABCDEF with A(0, 0), B(�2, 3), C(0, 4), D(3, 4), E(4, 2), F(3, 0) translated 2 units up and 1 unit to the left
1�2
Skills PracticeTransformations on the Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-24-2
© Glencoe/McGraw-Hill 221 Glencoe Algebra 1
Less
on
4-2
Identify each transformation as a reflection, translation, dilation, or rotation.
1. 2. 3.
4. 5. 6.
For Exercises 7–10, complete parts a and b.a. Find the coordinates of the vertices of each figure after the given
transformation is performed.b. Graph the preimage and its image.
7. triangle ABC with A(1, 2), B(4, �1), and 8. parallelogram PQRS with P(�2, �1),C(1, �1) reflected over the y-axis Q(3, �1), R(2, �3), and S(�3, �3)
translated 3 units up
9. trapezoid JKLM with J(�2, 1), K(2, 1), 10. triangle STU with S(3, 3), T(5, 1), and L(1, �1), and M(�1, �1) dilated by a U(1, 1) rotated 90° counterclockwise scale factor of 2 about the origin
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M�
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RS
x
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BCx
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© Glencoe/McGraw-Hill 222 Glencoe Algebra 1
Identify each transformation as a reflection, translation, dilation, or rotation.
1. 2. 3.
For Exercises 4–6, complete parts a and b.a. Find the coordinates of the vertices of each figure after the given
transformation is performed.b. Graph the preimage and its image.
4. triangle DEF with D(2, 3), 5. trapezoid EFGH with 6. triangle XYZ with X(3, 1),E(4, 1), and F(1, �1) E(3, 2), F(3, �3), Y(4, �2), and Z(1, �3) translated 4 units left G(1, �2), and H(1, 1) rotated 90° counterclockwiseand 3 units down reflected over the y-axis about the origin
GRAPHICS For Exercises 7–9, use the diagram at the right and the following information.
A designer wants to dilate the rocket by a scale factor of , and then translate it 5 units up.
7. Write the coordinates for the vertices of the rocket.
8. Find the coordinates of the final position of the rocket.
9. Graph the image on the coordinate plane.
10. DESIGN Ramona transformed figure ABCDEF to design a pattern for a quilt. Name two different sets of transformations she could have used to design the pattern.
AB
CD
E
F
x
y
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1�2
AB
C
DE
F
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Practice Transformations on the Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-24-2
Reading to Learn MathematicsTransformations on the Coordinate Plane
NAME ______________________________________________ DATE ____________ PERIOD _____
4-24-2
© Glencoe/McGraw-Hill 223 Glencoe Algebra 1
Less
on
4-2
Pre-Activity How are transformations used in computer graphics?
Read the introduction to Lesson 4-2 at the top of page 197 in your textbook.
In the sentence, “Computer graphic designers can create movement thatmimics real-life situations,” what phrase indicates the use oftransformations?
Reading the Lesson
1. Suppose you look at a diagram that shows two figures ABCDE and A�B�C�D�E�. If onefigure was obtained from the other by using a transformation, how do you tell which wasthe original figure?
2. Write the letter of the term and the Roman numeral of the figure that best matches eachstatement.
a. A figure is flipped over a line. A. dilation I.
b. A figure is turned around a point. B. translation II.
c. A figure is enlarged or reduced. C. reflection III.
d. A figure is slid horizontally, vertically, D. rotation IV.or both.
Helping You Remember
3. Give examples of things in everyday life that can help you remember what reflections,dilations, and rotations are.
© Glencoe/McGraw-Hill 224 Glencoe Algebra 1
The Legendary City of Ur The city of Ur was founded more than five thousand years ago inMesopotamia (modern-day Iraq). It was one of the world’s first cities.Between 1922 and 1934, archeologists discovered many treasures fromthis ancient city. A large cemetery from the 26th century B.C. wasfound to contain large quantities of gold, silver, bronze, and jewels. Themany cultural artifacts that were found, such as musical instruments,weapons, mosaics, and statues, have provided historians with valuableclues about the civilization that existed in early Mesopotamia.
1. Suppose that the ordered pairs below represent the volume (cm3) and mass (grams) of ten artifacts from the city of Ur. Plot each point on the graph.A(10, 150) B(150, 1350) C(200, 1760) D(50, 525) E(100, 1500) F(10, 88) G(200, 2100) H(150, 1675) I(100, 900) J(50, 440)
2. The equation relating mass, density, and volume for silver is m � 10.5V. Which of the points in Exercise 1 are solutions for this equation?
3. Suppose that the equation m � 8.8V relates mass, density, andvolume for the kind of bronze used in the ancient city of Ur. Whichof the points in Exercise 1 are solutions for this equation?
4. Explain why the graph in Exercise 1 shows only quadrant 1.
AF
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Enrichment
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Study Guide and InterventionRelations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-34-3
© Glencoe/McGraw-Hill 225 Glencoe Algebra 1
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Represent Relations A relation is a set of ordered pairs. A relation can berepresented by a set of ordered pairs, a table, a graph, or a mapping. A mapping illustrateshow each element of the domain is paired with an element in the range.
Express the relation{(1, 1), (0, 2), (3, �2)} as a table, agraph, and a mapping. State thedomain and range of the relation.
The domain for this relation is {0, 1, 3}.The range for this relation is {�2, 1, 2}.
X Y
103
12
�2
x
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O
x y
1 1
0 2
3 �2
A person playingracquetball uses 4 calories per hour forevery pound he or she weighs.
a. Make a table to show the relation between weight and calories burned in onehour for people weighing 100, 110, 120, and 130 pounds.Source: The Math Teacher’s Book of Lists
b. Give the domain and range.domain: {100, 110, 120, 130}range: {400, 440, 480, 520}
c. Graph the relation.
Weight (pounds)
Cal
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100 1200
520
480
440
400
x
y
x y
100 400
110 440
120 480
130 520
Example 1Example 1 Example 2Example 2
ExercisesExercises
1. Express the relation{(�2, �1), (3, 3), (4, 3)} as a table, a graph, and amapping. Then determinethe domain and range.
2. The temperature in a house drops 2° for every hour the air conditioner is on between the hours of 6 A.M. and 11 A.M.Make a graph to show the relationship between time andtemperature if the temperature at 6 A.M. was 82°F.
Time (A.M.)
Tem
per
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�F)
6 87 9 10 11 120
86
84
82
80
78
76
74
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© Glencoe/McGraw-Hill 226 Glencoe Algebra 1
Inverse Relations The inverse of any relation is obtained by switching the coordinatesin each ordered pair.
Express the relation shown in the mapping as a set of orderedpairs. Then write the inverse of the relation.
Relation: {(6, 5), (2, 3), (1, 4), (0, 3)}Inverse: {(5, 6), (3, 2), (4, 1), (3, 0)}
Express the relation shown in each table, mapping, or graph as a set of orderedpairs. Then write the inverse of each relation.
1. 2.
3. 4.
5. 6.
x
y
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�2014
�1467
x y
�3 5
�2 �1
1 0
2 4
X Y
�1245
�8�1
02
x y
�2 4
�1 3
2 1
4 5
X Y
6210
345
Study Guide and Intervention (continued)
Relations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-34-3
ExampleExample
ExercisesExercises
Skills PracticeRelations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-34-3
© Glencoe/McGraw-Hill 227 Glencoe Algebra 1
Less
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Express each relation as a table, a graph, and a mapping. Then determine thedomain and range.
1. {(�1, �1), (1, 1), (2, 1), (3, 2)}
2. {(0, 4), (�4, �4), (�2, 3), (4, 0)}
3. {(3, �2), (1, 0), (�2, 4), (3, 1)}
Express the relation shown in each table, mapping, or graph as a set of orderedpairs. Then write the inverse of the relation.
4. 5. 6.
x
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9�5
4
7682
x y
3 �5
�4 3
7 6
1 �2
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31
�2
�2041x
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0�4�2
4
4�4
30x
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�1123
�112x
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O
© Glencoe/McGraw-Hill 228 Glencoe Algebra 1
Express each relation as a table, a graph, and a mapping. Then determine thedomain and range.
1. {(4, 3), (�1, 4), (3, �2), (2, 3), (�2, 1)}
Express the relation shown in each table, mapping, or graph as a set of orderedpairs. Then write the inverse of the relation.
2. 3. 4.
BASEBALL For Exercises 5 and 6, use the graph that shows the batting average for Barry Bonds of the SanFrancisco Giants. Source: www.sportsillustrated.cnn.com
5. Find the domain and estimate the range.
6. Which seasons did Bonds have the lowest and highest batting averages?
METEORS For Exercises 7 and 8, use the table that shows the number of meteorsAnn observed each hour during a meteor shower.
7. What are the domain and range?
8. Graph the relation. Time (A.M.)
Meteor Shower
Nu
mb
er o
f M
eteo
rs
12–1 1–2 2–3 3–4 4–50
30
25
20
15
10
Time Number of (A.M.) Meteors
12 15
1 26
2 28
3 28
4 15
Year
Barry Bonds’ Batting
Ave
rag
e
’96 ’98’97 ’99 ’00 ’01 ’020
.34
.32
.30
.28
.26
x
y
O
X Y
5�5
37
9�6
48
x y
0 9
�8 3
2 �6
1 4
X Y
4�1
3�2
34
�21x
y
O
Practice Relations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-34-3
Reading to Learn MathematicsRelations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-34-3
© Glencoe/McGraw-Hill 229 Glencoe Algebra 1
Less
on
4-3
Pre-Activity How can relations be used to represent baseball statistics?
Read the introduction to Lesson 4-3 at the top of page 205 in your textbook.
In 1997, Ken Griffey, Jr. had home runs and strikeouts.
This can be represented with the ordered pair ( , ).
Reading the Lesson
1. Look at page 205 in your textbook. There you see the same relation represented by a setof ordered pairs, a table, a graph, and a mapping.
a. In the list of ordered pairs, where do you see the numbers for the domain? thenumbers for the range?
b. What parts of the table show the domain and the range?
c. How do the table, the graph, and the mapping show that there are three orderedpairs in the relation?
2. Which tells you more about a relation, a list of the ordered pairs in the relation or thedomain and range of the relation? Explain.
3. Describe how you would find the inverse of the relation {(1, 2), (2, 4), (3, 6), (4, 8)}.
Helping You Remember
4. The first letters in two words and their order in the alphabet can sometimes help youremember their mathematical meaning. Two key terms in this lesson are domain andrange. Describe how the alphabet method could help you remember their meaning.
© Glencoe/McGraw-Hill 230 Glencoe Algebra 1
Inverse RelationsOn each grid below, plot the points in Sets A and B. Then connect thepoints in Set A with the corresponding points in Set B. Then find theinverses of Set A and Set B, plot the two sets, and connect those points.
Set A Set B
(�4, 0) (0, 1)(�3, 0) (0, 2)(�2, 0) (0, 3)(�1, 0) (0, 4)
Set A Set B
(�3, �3) (�2, 1)(�2, �2) (�1, 2)(�1, �1) (0, 3)(0, 0) (1, 4)
Set A Set B
(�4, 1) (3, 2)(�3, 2) (3, 2)(�2, 3) (3, 2)(�1, 4) (3, 2)
13. What is the graphical relationship between the line segments you drewconnecting points in Sets A and B and the line segments connecting pointsin the inverses of those two sets?
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Enrichment
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4-34-3
InverseSet A Set B
1.
2.
3.
4.
InverseSet A Set B
5.
6.
7.
8.
InverseSet A Set B
9.
10.
11.
12.
Study Guide and InterventionEquations as Relations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-44-4
© Glencoe/McGraw-Hill 231 Glencoe Algebra 1
Less
on
4-4
Solve Equations The equation y � 3x � 4 is an example of an equation in twovariables because it contains two variables, x and y. The solution of an equation in twovariables is an ordered pair of replacements for the variables that results in a truestatement when substituted into the equation.
Find the solution set for y � �2x � 1, given the replacement set {(�2, 3), (0, �1), (1, �2), (3, 1)}.
Make a table. Substitute the x and y-values of eachordered pair into the equation.
x y y � �2x � 1 True or False
�2 33 � �2(�2) � 1
True3 � 3
0 �1�1 � �2(0) � 1
True�1 � �1
1 �2�2 � �2(1) � 1
False�2 � �3
3 11 � �2(3) � 1
False1 � �7
The ordered pairs (�2, 3), and (0, �1) result in truestatements. The solution set is {(�2, 3), (0, �1)}.
Solve b � 2a � 1 ifthe domain is {�2, �1, 0, 2, 4}.
Make a table. The values of a comefrom the domain. Substitute eachvalue of a into the equation todetermine the corresponding valuesof b in the range.
a 2a � 1 b (a, b)
�2 2(�2) � 1 �5 (�2, �5)
�1 2(�1) � 1 �3 (�1, �3)
0 2(0) � 1 �1 (0, �1)
2 2(2) � 1 3 (2, 3)
4 2(4) � 1 7 (4, 7)
The solution set is {(�2, �5),(�1, �3), (0, �1), (2, 3), (4, 7)}.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the solution set of each equation, given the replacement set.
1. y � 3x � 1; {(0, 1), � , 2�, ��1, � �, (�1, �2)}
2. 3x � 2y � 6; {(�2, 3), (0, 1), (0, �3), (2, 0)}
3. 2x � 5 � y; {(1, 3), (2, 1), (3, 2), (4, 3)}
Solve each equation if the domain is (�4, �2, 0, 2, 4}.
4. x � y � 4
5. y � �4x � 6
6. 5a � 2b � 10
7. 3x � 2y � 12
8. 6x � 3y � 18
9. 4x � 8 � 2y
10. x � y � 8
11. 2x � y � 10
2�3
1�3
© Glencoe/McGraw-Hill 232 Glencoe Algebra 1
Graph Solution Sets You can graph the ordered pairs in the solution set of anequation in two variables. The domain contains values represented by the independentvariable. The range contains the corresponding values represented by the dependentvariable, which are determined by the given equation.
Solve 4x � 2y � 12 if the domain is (�1, 0, 2, 4}. Graph the solution set.
First solve the equation for y in terms of x.4x � 2y � 12 Original equation
4x � 2y � 4x � 12 � 4x Subtract 4x from each side.
2y � 12 � 4x Simplify.
� Divide each side by 2.
y � 6 � 2x Simplify.
12 � 4x�2
2y�2
Study Guide and Intervention (continued)
Equations as Relations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-44-4
ExampleExample
Substitute each value of x from the domain todetermine the corresponding value of y in the range.
x 6 � 2x y (x, y )
�1 6 � 2(�1) 8 (�1, 8)
0 6 � 2(0) 6 (0, 6)
2 6 � 2(2) 2 (2, 2)
4 6 � 2(4) �2 (4, �2)
Graph the solution set.
x
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O
ExercisesExercises
Solve each equation for the given domain. Graph the solution set.
1. x � 2y � 4 for x � {�2, 0, 2, 4} 2. y � �2x � 3 for x � {�2, �1, 0, 1}
3. x � 3y � 6 for x � {�3, 0, 3, 6} 4. 2x � 4y � 8 for x � {�4, �2, 0, 2}
x
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Skills PracticeEquations as Relations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-44-4
© Glencoe/McGraw-Hill 233 Glencoe Algebra 1
Less
on
4-4
Find the solution set for each equation, given the replacement set.
1. y � 3x � 1; {(2, 5), (�2, 7), (0, �1), (1, 1)}
2. y � 2x � 4; {(�1, �2), (�3, 2), (1, 6), (�2, 8)}
3. y � 7 � 2x; {(3, 1), (4, �1), (5, �3), (�1, 5)}
4. �3x � y � 2; {(�3, 7), (�2, �4), (�1, �1), (3, 11)}
Solve each equation if the domain is {�2, �1, 0, 2, 5}.
5. y � x � 4
6. y � 3x � 2
7. y � 2x � 1
8. x � y � 2
9. x � 3 � y
10. 2x � y � 4
11. 2x � y � 7
12. 4x � 2y � 6
Solve each equation for the given domain. Graph the solution set.
13. y � 2x � 5 for x � {�5, �4, �2, �1, 0} 14. y � 2x � 3 for x � {�1, 1, 2, 3, 4}
15. 2x � y � 1 for x � {�2, �1, 0, 2, 3} 16. 2x � 2y � 6 for x � {�3, �1, 3, 4, 6}
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© Glencoe/McGraw-Hill 234 Glencoe Algebra 1
Find the solution set for each equation, given the replacement set.
1. y � 2 � 5x; {(3, 12), (�3, �17), (2, �8), (�1, 7)}
2. 3x � 2y � �1; {(�1, 1), (�2, �2.5), (�1, �1.5), (0, 0.5)}
Solve each equation if the domain is {�2, �1, 2, 3, 5}.
3. y � 4 � 2x
4. x � 8 � y
5. 4x � 2y � 10
6. 3x � 6y � 12
7. 2x � 4y � 16
8. x � y � 6
Solve each equation for the given domain. Graph the solution set.
9. 2x � 4y � 8 for x � {�4, �3, �2, 2, 5} 10. x � y � 1 for x � {�4, �3, �2, 0, 4}
EARTH SCIENCE For Exercises 11 and 12, use the following information.Earth moves at a rate of 30 kilometers per second around the Sun. The equation d � 30t relates the distance d inkilometers Earth moves to time t in seconds.
11. Find the set of ordered pairs when t � {10, 20, 30, 45, 70}.
12. Graph the set of ordered pairs.
GEOMETRY For Exercises 13–15, use the following information.
The equation for the area of a triangle is A � bh. Suppose the area of triangle DEF is 30 square inches.
13. Solve the equation for h.
14. State the independent and dependent variables.
15. Choose 5 values for b and find the corresponding values for h.
1�2
Time (s)
Distance Earth Travels
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tan
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km)
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Practice Equations as Relations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-44-4
Reading to Learn MathematicsEquations as Relations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-44-4
© Glencoe/McGraw-Hill 235 Glencoe Algebra 1
Less
on
4-4
Pre-Activity Why are equations of relations important in traveling?
Read the introduction to Lesson 4-4 at the top of page 212 in your textbook.
• In the equation p � 0.69d, p represents and d
represents .
• How many variables are in the equation p � 0.69d?
Reading the Lesson
1. Suppose you make the following table to solve an equation that uses the domain {�3, �2, �1, 0, 1}.
x x � 4 y (x, y)
�3 �3 � 4 �7 (�3, �7)
�2 �2 � 4 �6 (�2, �6)
�1 �1 � 4 �5 (�1, �5)
0 0 � 4 �4 (0, �4)
1 1 � 4 �3 (1, �3)
a. What is the equation?
b. Which column shows the domain?
c. Which column shows the range?
d. Which column shows the solution set?
2. The solution set of the equation y � 2x for a given domain is {(�2, �4), (0, 0), (2, 4), (7, 14)}. Tell whether each sentence is true or false. If false,replace the underlined word(s) to make a true sentence.
a. The domain contains the values represented by the independent variable.
b. The domain contains the numbers �4, 0, 4, and 14.
c. For each number in the domain, the range contains a corresponding number that is avalue of the dependent variable.
3. What is meant by “solving an equation for y in terms of x”?
Helping You Remember
4. Remember, when you solve an equation for a given variable, that variable becomes thedependent variable. Write an equation and describe how you would identify thedependent variable.
© Glencoe/McGraw-Hill 236 Glencoe Algebra 1
Coordinate Geometry and AreaHow would you find the area of a triangle whose vertices have the coordinates A(-1, 2), B(1, 4), and C(3, 0)?
When a figure has no sides parallel to either axis, the height and base are difficult to find.
One method of finding the area is to enclose the figure in a rectangle and subtract the area of the surrounding triangles from the area of the rectangle.
Area of rectangle DEFC� 4 � 4 � 16 square units
Area of triangle I � (2)(4) � 4
Area of triangle II � (2)(4) � 4
Area of triangle III � (2)(2) � 2
Total � 10 square units
Area of triangle ABC � 16 � 10, or 6 square units
Find the areas of the figures with the following vertices.
1. A(-4, -6), B(0, 4), 2. A(6, -2), B(8, -10), 3. A(0, 2), B(2, 7),C(4, 2) C(12, -6) C(6, 10), D(9, -2)
24 square units 20 square units 55 square units
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Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
4-44-4
Study Guide and InterventionGraphing Linear Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-54-5
© Glencoe/McGraw-Hill 237 Glencoe Algebra 1
Less
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Identify Linear Equations A linear equation is an equation that can be written inthe form Ax � By � C. This is called the standard form of a linear equation.
Standard Form of a Linear EquationAx � By � C, where A � 0, A and B are not both zero, and A, B, and C are integers whose GCF is 1.
Determine whether y � 6 � 3xis a linear equation. If so, write the equationin standard form.
First rewrite the equation so both variables are onthe same side of the equation.
y � 6 � 3x Original equation
y � 3x � 6 � 3x � 3x Add 3x to each side.
3x � y � 6 Simplify.
The equation is now in standard form, with A � 3,B � 1 and C � 6. This is a linear equation.
Determinewhether 3xy � y � 4 � 2x is alinear equation. If so, write theequation in standard form.
Since the term 3xy has two variables,the equation cannot be written in theform Ax � By � C. Therefore, this isnot a linear equation.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Determine whether each equation is a linear equation. If so, write the equation instandard form.
1. 2x � 4y 2. 6 � y � 8 3. 4x � 2y � �1
4. 3xy � 8 � 4y 5. 3x � 4 � 12 6. y � x2 � 7
7. y � 4x � 9 8. x � 8 � 0 9. �2x � 3 � 4y
10. 2 � x � y 11. y � 12 � 4x 12. 3xy � y � 8
13. 6x � 4y � 3 � 0 14. yx � 2 � 8 15. 6a � 2b � 8 � b
16. x � 12y � 1 17. 3 � x � x2 � 0 18. x2 � 2xy1�4
1�4
1�2
© Glencoe/McGraw-Hill 238 Glencoe Algebra 1
Graph Linear Equations The graph of a linear equation is a line. The line represents allsolutions to the linear equation. Also, every ordered pair on this line satisfies the equation.
Graph the equation y � 2x � 1.
Solve the equation for y.y � 2x � 1 Original equation
y � 2x � 2x � 1 � 2x Add 2x to each side.
y � 2x � 1 Simplify.
Select five values for the domain and make a table. Thengraph the ordered pairs and draw a line through the points.
x 2x � 1 y (x, y)
�2 2(�2) � 1 �3 (�2, �3)
�1 2(�1) � 1 �1 (�1, �1)
0 2(0) � 1 1 (0, 1)
1 2(1) � 1 3 (1, 3)
2 2(2) � 1 5 (2, 5)
Graph each equation.
1. y � 4 2. y � 2x 3. x � y � �1
4. 3x � 2y � 6 5. x � 2y � 4 6. 2x � y � �2
7. 3x � 6y � �3 8. �2x � y � �2 9. x � y � 6
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Study Guide and Intervention (continued)
Graphing Linear Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-54-5
ExampleExample
ExercisesExercises
Skills PracticeGraphing Linear Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-54-5
© Glencoe/McGraw-Hill 239 Glencoe Algebra 1
Less
on
4-5
Determine whether each equation is a linear equation. If so, write the equation instandard form.
1. xy � 6 2. y � 2 � 3x 3. 5x � y � 4
4. y � 2x � 5 5. y � �7 � 6x 6. y � 3x2 � 1
7. y � 4 � 0 8. 5x � 6y � 3x � 2 9. y � 1
Graph each equation.
10. y � 4 11. y � 3x 12. y � x � 4
13. y � x � 2 14. y � 4 � x 15. y � 4 � 2x
16. x � y � 3 17. 10x � �5y 18. 4x � 2y � 6
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© Glencoe/McGraw-Hill 240 Glencoe Algebra 1
Determine whether each equation is a linear equation. If so, write the equation instandard form.
1. 4xy � 2y � 9 2. 8x � 3y � 6 � 4x 3. 7x � y � 3 � y
4. 5 � 2y � 3x 5. 4y � x � 9x 6. a � b � 2
7. 6x � 2y 8. � � 1 9. � � 7
Graph each equation.
10. x � y � 2 11. 5x � 2y � 7 12. 1.5x � 3y � 9
COMMUNICATIONS For Exercises 13–15, use the following information.A telephone company charges $4.95 per month for longdistance calls plus $0.05 per minute. The monthly cost cof long distance calls can be described by the equation c � 0.05m � 4.95, where m is the number of minutes.
13. Find the y-intercept of the graph of the equation.
14. Graph the equation.
15. If you talk 140 minutes, what is the monthly cost for long distance?
MARINE BIOLOGY For Exercises 16 and 17, use the following information.Killer whales usually swim at a rate of 3.2–9.7 kilometers per hour, though they can travel up to 48.4 kilometers perhour. Suppose a migrating killer whale is swimming at anaverage rate of 4.5 kilometers per hour. The distance d thewhale has traveled in t hours can be predicted by theequation d � 4.5t.
16. Graph the equation.
17. Use the graph to predict the time it takes the killer whale to travel 30 kilometers.
Time (minutes)
Long Distance
Co
st (
$)
0 40 80 120 160
14
12
10
8
6
4
2
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y
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Practice Graphing Linear Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-54-5
Reading to Learn MathematicsGraphing Linear Equations
NAME ______________________________________________ DATE ____________ PERIOD _____
4-54-5
© Glencoe/McGraw-Hill 241 Glencoe Algebra 1
Less
on
4-5
Pre-Activity How can linear equations be used in nutrition?
Read the introduction to Lesson 4-5 at the top of page 218 in your textbook.
In the equation f � 0.3� �, what are the independent and dependent
variables?
Reading the Lesson
1. Describe the graph of a linear equation.
2. Determine whether each equation is a linear equation. Explain.
Equation Linear or non-linear? Explanation
a. 2x � 3y � 1
b. 4xy � 2y � 7
c. 2x2 � 4y � 3
d. � � 2
3. What do the terms x-intercept and y-intercept mean?
Helping You Remember
4. Describe the method you would use to graph 4x � 2y � 8.
4y�3
x�5
C�9
© Glencoe/McGraw-Hill 242 Glencoe Algebra 1
Taxicab GraphsYou have used a rectangular coordinate system to graph equations such as y � x � 1 on a coordinate plane. In a coordinate plane, the numbers in an ordered pair (x, y) can be any two real numbers.
A taxicab plane is different from the usual coordinate plane.The only points allowed are those that exist along the horizontal and vertical grid lines. You may think of the points as taxicabs that must stay on the streets.
The taxicab graph shows the equations y � �2 and y � x � 1.Notice that one of the graphs is no longer a straight line. It is now a collection of separate points.
Graph these equations on the taxicab plane at the right.
1. y � x � 1 2. y � �2x � 3
3. y � 2.5 4. x � �4
Use your graphs for these problems.
5. Which of the equations has the same graph in both the usual coordinate plane and the taxicab plane? x � �4
6. Describe the form of equations that have the same graph in both the usual coordinate plane and the taxicab plane.x � A and y � B, where A and B are integers
In the taxicab plane, distances are not measured diagonally, but along the streets.Write the taxi-distance between each pair of points.
7. (0, 0) and (5, 2) 8. (0, 0) and (-3, 2) 9. (0, 0) and (2, 1.5)7 units 5 units 3.5 units
10. (1, 2) and (4, 3) 11. (2, 4) and (-1, 3) 12. (0, 4) and (-2, 0)4 units 4 units 6 units
Draw these graphs on the taxicab grid at the right.
13. The set of points whose taxi-distance from (0, 0) is 2 units. indicated by crosses
14. The set of points whose taxi-distance from (2, 1) is 3 units. indicated by dots
x
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x
y
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x
y
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y � x � 1
y � �2
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
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Study Guide and InterventionFunctions
NAME ______________________________________________ DATE ____________ PERIOD _____
4-64-6
© Glencoe/McGraw-Hill 243 Glencoe Algebra 1
Less
on
4-6
Identify Functions Relations in which each element of the domain is paired withexactly one element of the range are called functions.
Determinewhether the relation {(6, �3),(4, 1), (7, �2), (�3, 1)} is afunction. Explain.
Since each element of the domain ispaired with exactly one element ofthe range, this relation is afunction.
Determine whether 3x � y � 6 is a function.
Since the equation is in the form Ax � By � C, the graph of theequation will be a line, as shownat the right.
If you draw a vertical line through each value of x, thevertical line passes through justone point of the graph. Thus, the line represents a function.
x
y
O
Example 1Example 1 Example 2Example 2
ExercisesExercises
Determine whether each relation is a function.
1. 2. 3.
4. 5. 6.
7. {(4, 2), (2, 3), (6, 1)} 8. {(�3, �3), (�3, 4), (�2, 4)} 9. {(�1, 0), (1, 0)}
10. �2x � 4y � 0 11. x2 � y2 � 8 12. x � �4
x
y
Ox
y
Ox
y
O
X Y
�1012
4567
x
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Ox
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O
© Glencoe/McGraw-Hill 244 Glencoe Algebra 1
Function Values Equations that are functions can be written in a form called functionnotation. For example, y � 2x �1 can be written as f(x) � 2x � 1. In the function, xrepresents the elements of the domain, and f(x) represents the elements of the range.Suppose you want to find the value in the range that corresponds to the element 2 in thedomain. This is written f(2) and is read “f of 2.” The value of f(2) is found by substituting 2 for x in the equation.
If f(x) � 3x � 4, find each value.
a. f(3)f(3) � 3(3) � 4 Replace x with 3.
� 9 � 4 Multiply.
� 5 Simplify.
b. f(�2)f(�2) � 3(�2) � 4 Replace x with �2.
� �6 � 4 Multiply.
� �10 Simplify.
If f(x) � 2x � 4 and g(x) � x2 � 4x, find each value.
1. f(4) 2. g(2) 3. f(�5)
4. g(�3) 5. f(0) 6. g(0)
7. f(3) � 1 8. f � � 9. g� �
10. f(a2) 11. f(k � 1) 12. g(2c)
13. f(3x) 14. f(2) � 3 15. g(�4)
1�4
1�4
Study Guide and Intervention (continued)
Functions
NAME ______________________________________________ DATE ____________ PERIOD _____
4-64-6
ExampleExample
ExercisesExercises
Skills PracticeFunctions
NAME ______________________________________________ DATE ____________ PERIOD _____
4-64-6
© Glencoe/McGraw-Hill 245 Glencoe Algebra 1
Less
on
4-6
Determine whether each relation is a function.
1. 2. 3.
4. 5. 6.
7. {(2, 5), (4, �2), (3, 3), (5, 4), (�2, 5)} 8. {(6, �1), (�4, 2), (5, 2), (4, 6), (6, 5)}
9. y � 2x � 5 10. y � 11
11. 12. 13.
If f(x) � 3x � 2 and g(x) � x2 � x, find each value.
14. f(4) 15. f(8)
16. f(�2) 17. g(2)
18. g(�3) 19. g(�6)
20. f(2) � 1 21. f(1) � 1
22. g(2) � 2 23. g(�1) � 4
24. f(x � 1) 25. g(3b)
x
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13
© Glencoe/McGraw-Hill 246 Glencoe Algebra 1
Determine whether each relation is a function.
1. 2. 3.
4. {(1, 4), (2, �2), (3, �6), (�6, 3), (�3, 6)} 5. {(6, �4), (2, �4), (�4, 2), (4, 6), (2, 6)}
6. x � �2 7. y � 2
If f(x) � 2x � 6 and g(x) � x � 2x2, find each value.
8. f(2) 9. f �� � 10. g(�1)
11. g�� � 12. f(7) � 9 13. g(�3) � 13
14. f(h � 9) 15. g(3y) 16. 2[g(b) � 1]
WAGES For Exercises 17 and 18, use the following information.
Martin earns $7.50 per hour proofreading ads at a local newspaper. His weekly wage w canbe described by the equation w � 7.5h, where h is the number of hours worked.
17. Write the equation in functional notation.
18. Find f(15), f(20), and f(25).
ELECTRICITY For Exercises 19–21, use the following information.
The table shows the relationship between resistance R and current I in a circuit.
19. Is the relationship a function? Explain.
20. If the relation can be represented by the equation IR � 12, rewrite the equation in functional notation so that the resistance R is a function of the current I.
21. What is the resistance in a circuit when the current is 0.5 ampere?
Resistance (ohms) 120 80 48 6 4
Current (amperes) 0.1 0.15 0.25 2 3
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Practice Functions
NAME ______________________________________________ DATE ____________ PERIOD _____
4-64-6
Reading to Learn MathematicsFunctions
NAME ______________________________________________ DATE ____________ PERIOD _____
4-64-6
© Glencoe/McGraw-Hill 247 Glencoe Algebra 1
Less
on
4-6
Pre-Activity How are functions used in meteorology?
Read the introduction to Lesson 4-6 at the top of page 226 in your textbook.
If pressure is the independent variable and temperature is the dependentvariable, what are the ordered pairs for this set of data?
Reading the Lesson
1. The statement, “Relations in which each element of the is paired with exactly one element of the are called functions,” is false. How can you change the underlined words to make the statement true?
2. Describe how each method shows that the relation represented is a function.
a. mapping
b. vertical line test
Helping You Remember
3. A student who was trying to help a friend remember how functions are different fromrelations that are not functions gave the following advice: Just remember that functionsare very strict and never give you a choice. Explain how this might help you rememberwhat a function is.
x
y
O
X Y
1237
�2�1
04
domainrange
© Glencoe/McGraw-Hill 248 Glencoe Algebra 1
Composite FunctionsThree things are needed to have a function—a set called the domain,a set called the range, and a rule that matches each element in thedomain with only one element in the range. Here is an example.
Rule: f(x) � 2x � 1f(x) � 2x � 1
f(1) � 2(1) � 1 � 2 � 1 � 3
f(2) � 2(2) � 1 � 4 � 1 � 5
f(-3) � 2(�3) � 1 � �6 � 1 � �5
Suppose we have three sets A, B, and C and two functions describedas shown below.
Rule: f(x) � 2x � 1 Rule: g( y) � 3y � 4g( y) � 3y � 4
g(3) � 3(3) � 4 � 5
Let’s find a rule that will match elements of set A with elements ofset C without finding any elements in set B. In other words, let’s finda rule for the composite function g[f(x)].
Since f(x) � 2x � 1, g[ f(x)] � g(2x � 1).Since g( y) � 3y � 4, g(2x � 1) � 3(2x � 1) � 4, or 6x � 1.Therefore, g[ f(x)] � 6x � 1.
Find a rule for the composite function g[f(x)].
1. f(x) � 3x and g( y) � 2y � 1 2. f(x) � x2 � 1 and g( y) � 4y
g[f(x)] � 6x � 1 g[f(x)] � 4x2 � 4
3. f(x) � �2x and g( y) � y2 � 3y 4. f(x) � and g( y) � y�1
g[f(x)] � 4x2 � 6x g[f(x)] � x � 3
5. Is it always the case that g[ f(x)] � f[ g(x)]? Justify your answer.
No. For example, in Exercise 1,f [g(x)] � f(2x � 1) � 3(2x � 1) � 6x � 3, not 6x � 1.
1�x � 3
1 3
x f(x)
5
g[f(x)]
A B C
1 3
2 5
–3 –5
x f(x)
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
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Study Guide and InterventionArithmetic Sequences
NAME ______________________________________________ DATE ____________ PERIOD _____
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© Glencoe/McGraw-Hill 249 Glencoe Algebra 1
Less
on
4-7
Recognize Arithmetic Sequences A sequence is a set of numbers in a specificorder. If the difference between successive terms is constant, then the sequence is called anarithmetic sequence.
Arithmetic Sequencea numerical pattern that increases or decreases at a constant rate or value called thecommon difference
Determine whether thesequence 1, 3, 5, 7, 9, 11, … is anarithmetic sequence. Justify youranswer.
If possible, find the common differencebetween the terms. Since 3 � 1 � 2,5 � 3 � 2, and so on, the common differenceis 2.
Since the difference between the terms of 1, 3, 5, 7, 9, 11, … is constant, this is anarithmetic sequence.
Determine whether thesequence 1, 2, 4, 8, 16, 32, … is anarithmetic sequence. Justify youranswer.
If possible, find the common differencebetween the terms. Since 2 � 1 � 1 and 4 � 2 � 2, there is no common difference.
Since the difference between the terms of 1, 2, 4, 8, 16, 32, … is not constant, this isnot an arithmetic sequence.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Determine whether each sequence is an arithmetic sequence. If it is, state thecommon difference.
1. 1, 5, 9, 13, 17, … 2. 8, 4, 0, �4, �8, … 3. 1, 3, 9, 27, 81, …
4. 10, 15, 25, 40, 60, … 5. �10, �5, 0, 5, 10, … 6. 8, 6, 4, 2, 0, �2, …
7. 4, 8, 12, 16, … 8. 15, 12, 10, 9, … 9. 1.1, 2.1, 3.1, 4.1, 5.1, …
10. 8, 7, 6, 5, 4, … 11. 0.5, 1.5, 2.5, 3.5, 4.5, … 12. 1, 4, 16, 64, …
13. 10, 14, 18, 22, … 14. �3, �6, �9, �12, … 15. 7, 0, �7, �14, …
© Glencoe/McGraw-Hill 250 Glencoe Algebra 1
Write Arithmetic Sequences You can use the common difference of an arithmeticsequence to find the next term of the sequence. Each term after the first term is found byadding the preceding term and the common difference.
Terms of an Arithmetic SequenceIf a1 is the first term of an arithmetic sequence with common difference d, then the sequence is a1, a1 � d, a1 � 2d, a1 � 3d, … .
nth Term of an Arithmetic Sequence an � a1 � (n � 1)d
Study Guide and Intervention (continued)
Arithmetic Sequences
NAME ______________________________________________ DATE ____________ PERIOD _____
4-74-7
Find the next threeterms of the arithmetic sequence 28,32, 36, 40, ….
Find the common difference bysubtracting successive terms.
The common difference is 4.Add 4 to the last given term, 40, to getthe next term. Continue adding 4 untilthe next three terms are found.
The next three terms are 44, 48, 52.
40
� 4 � 4 � 4
44 48 52
28
� 4 � 4 � 4
32 36 40
Write an equation for thenth term of the sequence 12, 15, 18, 21, … .
In this sequence, a1 is 12. Find the commondifference.
The common difference is 3.Use the formula for the nth term to write anequation.
an � a1 � (n � 1)d Formula for the nth term
an � 12 � (n � 1)3 a1 � 12, d � 3
an � 12 � 3n � 3 Distributive Property
an � 3n � 9 Simplify.
The equation for the nth term is an � 3n � 9.
12
� 3 � 3 � 3
15 18 21
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the next three terms of each arithmetic sequence.
1. 9, 13, 17, 21, 25, … 2. 4, 0, �4, �8, �12, … 3. 29, 35, 41, 47, …
4. �10, �5, 0, 5, … 5. 2.5, 5, 7.5, 10, … 6. 3.1, 4.1, 5.1, 6.1, …
Find the nth term of each arithmetic sequence described.
7. a1 � 6, d � 3, n � 10 8. a1 � �2, d � �3, n � 8 9. a1 � 1, d � �5, n � 20
10. a1 � �3, d � �2, n � 50 11. a1 � �12, d � 4, n � 20 12. a1 � 1, d � , n � 11
Write an equation for the nth term of the arithmetic sequence.
13. 1, 3, 5, 7, … 14. �1, �4, �7, �10, … 15. �4, �9, �14, �19, …
1�2
Skills PracticeArithmetic Sequences
NAME ______________________________________________ DATE ____________ PERIOD _____
4-74-7
© Glencoe/McGraw-Hill 251 Glencoe Algebra 1
Less
on
4-7
Determine whether each sequence is an arithmetic sequence. If it is, state thecommon difference.
1. 4, 7, 9, 12, … 2. 15, 13, 11, 9, …
3. 7, 10, 13, 16, … 4. �6, �5, �3, �1, …
5. �5, �3, �1, 1, … 6. �9, �12, �15, �18, …
Find the next three terms of each arithmetic sequence.
7. 3, 7, 11, 15, … 8. 22, 20, 18, 16, …
9. �13, �11, �9, �7, … 10. �2, �5, �8, �11, …
11. 19, 24, 29, 34, … 12. 16, 7, �2, �11, …
Find the nth term of each arithmetic sequence described.
13. a1 � 6, d � 3, n � 12 14. a1 � �2, d � 5, n � 11
15. a1 � 10, d � �3, n � 15 16. a1 � �3, d � �3, n � 22
17. a1 � 24, d � 8, n � 25 18. a1 � 8, d � �6, n � 14
19. 8, 13, 18, 23, … for n � 17 20. �10, �3, 4, 11, … for n � 12
21. 12, 10, 8, 6, … for n � 16 22. 12, 7, 2, �3, … for n � 25
Write an equation for the nth term of each arithmetic sequence. Then graph thefirst five terms of the sequence.
23. 7, 13, 19, 25, … 24. 30, 26, 22, 18, … 25. �7, �4, �1, 2, …
n
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20
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© Glencoe/McGraw-Hill 252 Glencoe Algebra 1
Determine whether each sequence is an arithmetic sequence. If it is, state thecommon difference.
1. 21, 13, 5, �3, … 2. �5, 12, 29, 46, … 3. �2.2, �1.1, 0.1, 1.3, …
Find the next three terms of each arithmetic sequence.
4. 82, 76, 70, 64, … 5. �49, �35, �21, �7, … 6. , , , 0, …
Find the nth term of each arithmetic sequence described.
7. a1 � 7, d � 9, n � 18 8. a1 � �12, d � 4, n � 36
9. �18, �13, �8, �3, … for n � 27 10. 4.1, 4.8, 5.5, 6.2, … for n � 14
11. a1 � , d � , n � 15 12. a1 � 2 , d � 1 , n � 24
Write an equation for the nth term of each arithmetic sequence. Then graph thefirst five terms of the sequence.
13. 9, 13, 17, 21, … 14. �5, �2, 1, 4, … 15. 19, 31, 43, 55, …
BANKING For Exercises 16 and 17, use the following information.
Chem deposited $115.00 in a savings account. Each week thereafter, he deposits $35.00 intothe account.
16. Write a formula to find the total amount Chem has deposited for any particular numberof weeks after his initial deposit.
17. How much has Chem deposited 30 weeks after his initial deposit?
18. STORE DISPLAY Tamika is stacking boxes of tissue for a store display. Each row oftissues has 2 fewer boxes than the row below. The first row has 23 boxes of tissues. Howmany boxes will there be in the tenth row?
2 4 6
60
40
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Practice Arithmetic Sequences
NAME ______________________________________________ DATE ____________ PERIOD _____
4-74-7
Reading to Learn MathematicsArithmetic Sequences
NAME ______________________________________________ DATE ____________ PERIOD _____
4-74-7
© Glencoe/McGraw-Hill 253 Glencoe Algebra 1
Less
on
4-7
Pre-Activity How are arithmetic sequences used to solve problems in science?
Read the introduction to Lesson 4-7 at the top of page 233 in your textbook.
Describe the pattern in the data.
Reading the Lesson
1. Do the recorded altitudes in the introduction form an arithmetic sequence? Explain.
2. What is meant by successive terms?
3. Complete the table.
PatternIs the sequence increasing Is there a common difference? or decreasing? If so, what is it?
a. 2, 5, 8, 11, 14, …
b. 55, 50, 45, 40, …
c. 1, 2, 4, 9, 16, …
d. , 0, � , �1, …
e. 2.6, 2.9, 3.2, 3.5, …
Helping You Remember
4. Use the pattern 3, 7, 11, 15, … to explain how you would help someone else learn how tofind the 10th term of an arithmetic sequence.
1�2
1�2
© Glencoe/McGraw-Hill 254 Glencoe Algebra 1
Arithmetic SeriesAn arithmetic series is a series in which each term after the first may befound by adding the same number to the preceding term. Let S stand forthe following series in which each term is 3 more than the preceding one.
S � 2 � 5 � 8 � 11 � 14 � 17 � 20
The series remains the same if we S � 2 � 5 � 8 � 11 � 14 � 17 � 20reverse the order of all the terms. So S � 20 � 17 � 14 � 11 � 8 � 5 � 2let us reverse the order of the terms 2S � 22 � 22 � 22 � 22 � 22 � 22 � 22and add one series to the other, term 2S � 7(22)by term. This is shown at the right.
S � � 7(11) � 77Let a represent the first term of the series.Let � represent the last term of the series.Let n represent the number of terms in the series.
In the preceding example, a � 2, l � 20, and n � 7. Notice that whenyou add the two series, term by term, the sum of each pair of terms is 22.That sum can be found by adding the first and last terms, 2 � 20 or a � �. Notice also that there are 7, or n, such sums. Therefore, the valueof 2S is 7(22), or n(a � �) in the general case. Since this is twice the sumof the series, you can use the following formula to find the sum of anyarithmetic series.
S �
Find the sum: 1 � 2 � 3 � 4 � 5 � 6 � 7 � 8 � 9
a � 1, � � 9, n � 9, so S � � � 45
Find the sum: �9 � (�5) � (�1) � 3 � 7 � 11 � 15
a � 29, � � 15, n � 7, so S � � � 21
Find the sum of each arithmetic series.
1. 3 � 6 � 9 � 12 � 15 � 18 � 21 � 24
2. 10 � 15 � 20 � 25 � 30 � 35 � 40 � 45 � 50
3. �21 � (�16) � (�11) � (�6) � (�1) � 4 � 9 � 14
4. even whole numbers from 2 through 100
5. odd whole numbers between 0 and 100
7 6�2
7(�9 � 15)��2
9 10�2
9(1 � 9)��2
n(a � �)��2
7(22)�2
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
4-74-7
Example 1Example 1
Example 2Example 2
Study Guide and InterventionWriting Equations from Patterns
NAME ______________________________________________ DATE ____________ PERIOD _____
4-84-8
© Glencoe/McGraw-Hill 255 Glencoe Algebra 1
Less
on
4-8
Look for Patterns A very common problem-solving strategy is to look for a pattern.Arithmetic sequences follow a pattern, and other sequences can follow a pattern.
Find the next threeterms in the sequence 3, 9, 27, 81, … .
Study the pattern in the sequence.
Successive terms are found bymultiplying the last given term by 3.
The next three terms are 243, 729, 2187.
81
� 3 � 3 � 3
243 729 2187
3
� 3 � 3 � 3
9 27 81
Find the next three termsin the sequence 10, 6, 11, 7, 12, 8, … .
Study the pattern in the sequence.
Assume that the pattern continues.
The next three terms are 13, 9, 14.
8
� 5 � 4 � 5
13 9 14
� 4 � 5
10 6 11
� 4 � 5
7 12
� 4
8
Example 1Example 1 Example 2Example 2
ExercisesExercises
1. Give the next two items for the pattern below.
Give the next three numbers in each sequence.
2. 2, 12, 72, 432, … 3. 7, �14, 28, �56, …
4. 0, 10, 5, 15, 10, … 5. 0, 1, 3, 6, 10, …
6. x � 1, x � 2, x � 3, … 7. x, , , , …x�4
x�3
x�2
© Glencoe/McGraw-Hill 256 Glencoe Algebra 1
Write Equations Sometimes a pattern can lead to a general rule that can be written asan equation.
Suppose you purchased a number of packages of blank compactdisks. If each package contains 3 compact disks, you could make a chart to showthe relationship between the number of packages of compact disks and thenumber of disks purchased. Use x for the number of packages and y for thenumber of compact disks.
Make a table of ordered pairs for several points of the graph.
The difference in the x values is 1, and the difference in the y values is 3. This patternshows that y is always three times x. This suggests the relation y � 3x. Since the relation isalso a function, we can write the equation in functional notation as f(x) � 3x.
1. Write an equation for the function in 2. Write an equation for the function infunctional notation. Then complete functional notation. Then complete the table. the table.
3. Write an equation in functional notation. 4. Write an equation in functional notation.
x
y
Ox
y
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x �2 �1 0 1 2 3
y 10 7 4
x �1 0 1 2 3 4
y �2 2 6
Number of Packages 1 2 3 4 5
Number of CDs 3 6 9 12 15
Study Guide and Intervention (continued)
Writing Equations from Patterns
NAME ______________________________________________ DATE ____________ PERIOD _____
4-84-8
ExampleExample
ExercisesExercises
Skills PracticeWriting Equations from Patterns
NAME ______________________________________________ DATE ____________ PERIOD _____
4-84-8
© Glencoe/McGraw-Hill 257 Glencoe Algebra 1
Less
on
4-8
Find the next two items for each pattern. Then find the 19th figure in the pattern.
1.
2.
Find the next three terms in each sequence.
3. 1, 4, 10, 19, 31, … 4. 15, 14, 16, 15, 17, 16, …
5. 29, 28, 26, 23, 19, … 6. 2, 3, 2, 4, 2, 5, …
7. x, x � 1, x � 2, … 8. y, 4y, 9y, 16y, …
Write an equation in function notation for each relation.
9. 10. 11.
12. 13. 14.
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© Glencoe/McGraw-Hill 258 Glencoe Algebra 1
1. Give the next two items for the pattern. Then find the 21st figure in the pattern.
Find the next three terms in each sequence
2. �5, �2, �3, 0, �1, 2, 1, 4, … 3. 0, 1, 3, 6, 10, 15, …
4. 0, 1, 8, 27, … 5. 3, 2, 4, 3, 5, 4, …
6. a � 1, a � 4, a � 9, … 7. 3d � 1, 4d � 2, 5d � 3, …
Write an equation in function notation for each relation.
8. 9. 10.
BIOLOGY For Exercises 11 and 12, use the following information.
Male fireflies flash in various patterns to signal location and perhaps to ward off predators.Different species of fireflies have different flash characteristics, such as the intensity of theflash, its rate, and its shape. The table below shows the rate at which a male firefly is flashing.
11. Write an equation in function notation for the relation.
12. How many times will the firefly flash in 20 seconds?
13. GEOMETRY The table shows the number of diagonals that can be drawn from one vertex in a polygon. Write anequation in function notation for the relation and find thenumber of diagonals that can be drawn from one vertex in a 12-sided polygon.
Sides 3 4 5 6
Diagonals 0 1 2 3
Time (seconds) 1 2 3 4 5
Number of Flashes 2 4 6 8 10
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Practice Writing Equations from Patterns
NAME ______________________________________________ DATE ____________ PERIOD _____
4-84-8
Reading to Learn MathematicsWriting Equations From Patterns
NAME ______________________________________________ DATE ____________ PERIOD _____
4-84-8
© Glencoe/McGraw-Hill 259 Glencoe Algebra 1
Less
on
4-8
Pre-Activity Why is writing equations from patterns important in science?
Read the introduction to Lesson 4-8 at the top of page 240 in your textbook.
• What is meant by the term linear pattern?
• Describe any arithmetic sequences in the data.
Reading the Lesson
1. What is meant by the term inductive reasoning?
2. For the figures below, explain why Figure 5 does not follow the pattern.
3. Describe the steps you would use to find the pattern in the sequence 1, 5, 25, 125, … .
Helping You Remember
4. What are some basic things to remember when you are trying to discover whether thereis a pattern in a sequence of numbers?
1 2 3 4 5
© Glencoe/McGraw-Hill 260 Glencoe Algebra 1
Traceable FiguresTry to trace over each of the figures below without tracing the samesegment twice.
The figure at the left cannot be traced, but the one at the right can.The rule is that a figure is traceable if it has no points, or exactly twopoints where an odd number of segments meet. The figure at the lefthas three segments meeting at each of the four corners. However, thefigure at the right has exactly two points, L and Q, where an oddnumber of segments meet.
Determine whether each figure can be traced. If it can, thenname the starting point and number the sides in the order inwhich they should be traced.
1. 2.
3. 4.
E
A B C
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Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
4-84-8
Chapter 4 Test, Form 1
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 261 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1 and 2, use the graph to answer each question.
1. Write the ordered pair for point J.A. (1, �2) B. (2, 1)C. (1, 2) D. (2, �1) 1.
2. Name the quadrant in which point J is located.A. I B. II C. III D. IV 2.
3. To plot the point (1, �2), start at the origin and moveA. left 1 unit and down 2 units. B. left 2 units and down 1 unit.C. left 2 units and up 1 unit. D. right 1 unit and down 2 units. 3.
4. Which best describes a dilation?A. a flip B. an enlargement or reductionC. a slide D. a turn around a point 4.
5. Determine what type or transformation is shown.A. translation B. rotationC. reflection D. dilation 5.
6. A line segment with end points at point M(�2, 0) and N(�1, 2) is translated 4 units left. What are the coordinates of the endpoints after the transformation is performed?A. M�(�6, �4), N�(�5, �2) B. M�(�6, 0), N�(�5, 2)C. M�(�2, �4), N�(�1, �2) D. M�(2, 0), N�(3, 2) 6.
7. Which table, mapping, or graph does not show the relation {(�1, 1), (1, 2), (2, �2), (4, 3)}?A. B.
C. D. 7.
8. What is the inverse of the relation {(0, 1), (1, 0), (3, �4)}?A. {(0, 0), (1, 1), (3, �4)} B. {(0, 1), (1, 0), (3, �4)}C. {(1, 0), (0, 1), (4, �3)} D. {(1, 0), (0, 1), (�4, 3)} 8.
9. Solve the equation y � 3x if the domain is {�1, 0, 1}.A. {(�3, �1), (0, 0), (3, 1)} B. {(�1, �3), (0, 0), (1, 3)}C. {(�1, 2), (0, 3), (1, 4)} D. {(�1, �1), (0, 0), (1, 1)} 9.
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© Glencoe/McGraw-Hill 262 Glencoe Algebra 1
10. The distance d a car travels in t hours is given by the function d � 55t.Find d when t � 5.A. 275 B. 11 C. 60 D. 50 10.
11. Which equation is a linear equation?
A. 4m2 � 6 B. 3a � 5b � �3 C. �23�xy � �
34�y � 0 D. x2 � y2 � 0 11.
12. Which line shown at the right is the graph of y � 2x � 4?A. l B. the x-axisC. p D. q 12.
13. Determine which relation is a function.A. B.
C. y � �15�x � 2 D. {(3, 0), (�2, �2), (7, �2), (�2, 0)} 13.
14. Determine which relation is a function.A. {(1, 1), (1, 2)} B. x � 5 � 1 C. y � 9 D. x � 2 14.
15. If h(r) � �23�r � 6, what is the value of h(�9)?
A. 12 B. 0 C. �12 D. �6�23� 15.
16. Determine which sequence is an arithmetic sequence.
A. 3, 6, 12, 24, … B. �15�, �
17�, �
19�, �1
11�
, …
C. �7, �3, 1, 5, … D. �10, 5, ��52�, �
54�, … 16.
17. Find the next three terms of the arithmetic sequence 5, 9, 13, 17, … .A. 21 B. 21, 25, 29 C. 41, 45, 49 D. 21, 41, 61 17.
18. Find the next two numbers of the sequence 1, 2, 4, 8, 16, … .A. 32, 64 B. 24, 32 C. 20, 22 D. 18, 20 18.
19. Find the next item in the pattern, .
A. B. C. D. 19.
20. Write an equation in function notation for the relation at the right.A. f(x) � 2x B. f(x) � �xC. f(x) � x � 1 D. f(x) � 1 � x 20.
Bonus Solve y � x � 3 if the domain is {0, 1, 2, 3}.Graph the equation y � x � 3. B:
X
12
34
5�2
Y
NAME DATE PERIOD
44 Chapter 4 Test, Form 1 (continued)
y
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x 3 4 4 5
y �1 2 3 6
Chapter 4 Test, Form 2A
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 263 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1 and 2, use the graph to answer each question.
1. Write the ordered pair for point I.A. (1, �4) B. (�1, 4)C. (�4, 1) D. (4, �1) 1.
2. Name the quadrant in which point K is located.A. I B. II C. III D. IV 2.
3. To plot the point (�7, 4), start at the origin and moveA. left 7 units and down 4 units. B. left 4 units and down 7 units.C. left 7 units and up 4 units. D. left 4 units and up 7 units. 3.
4. What type of transformation is shown at the right?A. reflection B. translationC. dilation D. rotation 4.
5. The letter P is flipped over a line. Which transformation is this? A. reflection B. translation C. dilation D. rotation 5.
6. Triangle ABC with A(�4, �1), B(�2, �1), and C(�4, 4) is rotated 180�about the origin. What are the coordinates of the vertices of the figure after the triangle is rotated?A. A�(�1, 4), B�(�1, 2), C�(4, 4) B. A�(�1, �4), B�(�1, �2), C�(4, �4)C. A�(4, 1), B�(2, 1), C�(4, �4) D. A�(4, �1), B�(2, �1), C�(4, 4) 6.
7. State the range of the relation {(�2, 5), (0, �1), (�1, 4), (�1, 5)}.A. {�2, 0, �1} B. {�1, 4, 5} C. {�2, 0} D. {�1, 4} 7.
8. What is the inverse of the relation {(3, �1), (2, 5), (�3, 4), (�2, 0)}?A. {(�3, 1), (�2, �5), (3, �4), (2, 0)} B. {(�2, 0), (�3, 4), (2, 5), (3, �1)} C. {(�1, 3), (5, 2), (4, �3), (0, �2)} D. {(1, �3), (�5, �2), (�4, 3), (0, 2)} 8.
9. Solve y � 2x � 7 if the domain is {�3, 1, 5}.A. {(�3, �1), (1, �9), (5, �17)} B. {(�3, �10), (1, �6), (5, �2)}C. {(�3, �13), (1, �5), (5, 3)} D. {(�3, �6), (1, 2), (5, 10)} 9.
10. Which equation is not a linear equation?
A. �4v � 2w � 7 B. �4x
� � y C. x � �5 D. �2x� � �
3y� � 6 10.
11. If g(x) � 3x2�4x � 1, what is the value of g(�2)?A. 21 B. 29 C. 45 D. 5 11.
12. Find the next two numbers of the sequence 7, 11, 8, 12, 9, 13, 10, … .A. 11, 15 B. 14, 15 C. 14, 11 D. 15, 12 12.
44
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© Glencoe/McGraw-Hill 264 Glencoe Algebra 1
Chapter 4 Test, Form 2A (continued)
13. Which is the graph of 2x � y � 1 if the domain is {�2, �1, 0, 1, 2}?A. B. C. D. 13.
14. Which line shown at the right is the graph of x � 2y � 4?A. l B. mC. p D. q 14.
15. Which equation has a graph that is a vertical line?A. 2x � y B. 3x � 2 � 0C. y � 5 � 3 D. x � y � 0 15.
16. Determine which relation is not a function.A. B.
C. D. 16.
17. Determine which sequence is not an arithmetic sequence.
A. �7, 0, 7, 14, … B. 0, �12�, 1, �
32�, … C. 10, 6, 2, �2, … D. 2, 4, 8, 16, … 17.
18. Which equation describes the nth term of the arithmetic sequence 7, 10, 13, 16, …?A. an � 3n � 4 B. an � 7 � 3n C. an � �4n � 3 D. an � 3n�4 18.
19. Find the next two items in the pattern .
A. B. C. D. 19.
20. Write an equation in function notation for the relation shown at the right.A. f(x)��2x B. f(x) � x�2C. f(x) � 2x � 2 D. f(x) � �x � 2 20.
Bonus Find the solution set of 2x � y2 � 8, given the replacement set {(2, �2), (6, 2), (6, 22), (4, 0), (12, �4)}. B:
X
0
2
9
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56
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2�3
95
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NAME DATE PERIOD
44
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x �2 0 1 3
y 0 0 2 1
Chapter 4 Test, Form 2B
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 265 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1 and 2, use the graph to answer each question.
1. Write the ordered pair for point L.A. (1, �4) B. (�4, 1)C. (�1, �4) D. (�4, �1) 1.
2. Name the quadrant in which point E is located.A. I B. II C. III D. IV 2.
3. To plot the point (�5, 2), start at the origin and moveA. right 2 units and down 5 units. B. left 5 units and up 2 units.C. left 5 units and down 2 units. D. right 2 units and up 5 units. 3.
4. What type of transformation is shown at the right?A. reflection B. translationC. dilation D. rotation 4.
5. A letter R is turned around a point. Which type of transformation is this?A. reflection B. translation C. dilation D. rotation 5.
6. Triangle HIJ with H(�2, 1), I(1, 4), and J(3, 1) is reflected over the x-axis.What are the coordinates of the vertices of the figure after the triangle is reflected?A. H�(�2, �1), I�(1, �4), J�(3, �1) B. H�(2, 1), I�(�1, 4), J�(�3, 1)C. H�(2, �1), I�(�1,�4), J�(�3, �1) D. H�(1, �2), I�(4, 1), J�(1, 3) 6.
7. What is the range of the relation {(5, 3), (2, 8), (�1, 1), (6, 1)}?A. {(�1, 1), (6, 1)} B. {�1, 2, 5, 6}C. {1, 3, 8} D. {3, 8} 7.
8. What is the inverse of the relation {(�2, �1), (2, 1), (�2, 4), (�4, 0)}?A. {(�4, 0), (�2, 4), (2, 1), (�2, �1)} B. {(2, 1), (�2, �1), (2, �4), (4, 0)} C. {(1, 2), (�1, �2), (�4, 2), (0, 4)} D. {(�1, �2), (1, 2), (4, �2), (0, �4)} 8.
9. Solve y � �2x � 8 if the domain is {�2, 0, 4}.A. {(�2, 12), (0, 8), (4, 0)} B. {(�2, 4), (0, 8), (4, 0)}C. {(�2, 6), (0, 8), (4, 12)} D. {(�2, 4), (0, 0), (4, �8)} 9.
10. Which equation is not a linear equation?
A. 2x � 5y � 3 B. y � �10 C. 5 � 3xy D. y � �7x
� � 4 10.
11. If f(x) � 2x2�3x � 5, what is the value of f(�3)?A. 14 B. 50 C. 2 D. 32 11.
12. Find the next two numbers of the sequence 1, 8, 5, 12, 9, 16, 13, … .A. 24, 21 B. 20, 17 C. 20, 24 D. 17, 21 12.
44
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© Glencoe/McGraw-Hill 266 Glencoe Algebra 1
Chapter 4 Test, Form 2B (continued)
13. Which is the graph of 2x � y � �5 if the domain is {�4, �3, �2, �1, 0}?A. B. C. D. 13.
14. Which line shown at the right is the graph of x � 2y � 6?A. r B. sC. t D. v 14.
15. Which equation has a graph that is a horizontal line?A. x � 7 � 0 B. x � yC. 2y � 3 � 4 D. x � y � 0 15.
16. Determine which relation is a function.A. B. C. D. 16.
17. Determine which sequence is an arithmetic sequence.A. �16, �12, �8, �4, … B. 1, 4, 2, 5, 3, …C. 4, 8, 16, 32, … D. 1, 1, 2, 3, 5, … 17.
18. Which equation describes the nth term of the arithmetic sequence �12, �14, �16, �18, …?A. an � �2n�10 B. an � �12�2nC. an � 10n�2 D. an � �2n � 10 18.
19. Find the next two items in the pattern, .
A. B. C. D. 19.
20. Write an equation in function notation for the relation.A. f(x) � �2x B. f(x) � �x � 2C. f(x) � x�2 D. f(x) � 2x � 2 20.
Bonus If f(x) � x � x2, find f(2m � 3). B:
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3
�1
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NAME DATE PERIOD
44
r s
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x y�2 7
0 0
1 �2
1 3
Chapter 4 Test, Form 2C
© Glencoe/McGraw-Hill 267 Glencoe Algebra 1
Write the ordered pair for each point 1.shown at the right. Name the quadrant in which the point is located. 2.
1. S 2. T 3.3. U 4–6.
Plot each point on a coordinate plane.
4. A(3, 2) 5. B(0, �2) 6. C(�3, 4)
For Questions 7 and 8, determine whether each transformation is a reflection, translation, dilation, or rotation.
7. 8.
9. Express the relation {(1, 4), (�2, 3), (�5, 0), (7, 4), (3, 2)} asa mapping. Then determine the domain and range.
10. Express the relation shown in the graph as a set of ordered pairs.Then write the inverse of the relation.
11. Find the solution set for x � 2y � 9,given the replacement set {(�1, �5), (3, �3), (5, 2), (7, 1)}.
12. Solve y � �2x � 1 if the domain is {�2, �1, 0, 1, 2}.Graph the solution set.
For Questions 13 and 14, determine whether each equation is a linear equation. If so, write the equation in standard form.
13. xy � 6 14. 2x � 3y � 7 � 3
15. Graph the equation x � 4y � 2.
y
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NAME DATE PERIOD
SCORE 44
Ass
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y
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7.
8.
9.
10.
11.
12.
13.
14.
15. y
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© Glencoe/McGraw-Hill 268 Glencoe Algebra 1
Chapter 4 Test, Form 2C (continued)
Determine whether each relation is a function.
16. 17.
For Questions 18 and 19, if f(x) � x2 � 3x � 2, find each value.
18. f(2) 19. f(5v)
20. Determine whether the sequence �10, �7, �4, �1, … is an arithmetic sequence. If so, state the common difference.
21. Find the next three terms of the arithmetic sequence 8, 15, 22, 29, ….}.
22. Write an equation for the nth term of the sequence 12, 5, �2, �9, … . Then graph the first five terms of the sequence.
23. Find the next two items in the pattern,
24. Use the table below that shows the amount of gasoline a car consumes for different distances driven.
Write an equation in function notation for the relationship between distance and gasoline used.
25. Maya wants to enlarge a rectangular cartoon that is 2 inches wide and 3 inches tall by a scale factor of 1.5.What will be the dimensions of the new cartoon? Use a coordinate system to draw a picture of the original cartoon and the enlarged cartoon. Place one corner of each cartoon at the origin and for each cartoon write the coordinates of the other three vertices.
Bonus Graph x � 3, y � �1, and 2x � 2y � 0 on a coordinate plane. Give the vertices of the figure formed by the three lines.
.
y
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7�3
42
3�2
4
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NAME DATE PERIOD
44
distance (mi) 1 2 3 4 5
gasoline (gal) 0.04 0.08 0.12 0.16 0.20
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
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2 4 5
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Chapter 4 Test, Form 2D
© Glencoe/McGraw-Hill 269 Glencoe Algebra 1
Write the ordered pair for each point 1.shown at the right. Name the quadrant in which the point is located. 2.
1. M 2. N 3.
3. P 4–6.
Plot each point on a coordinate plane.
4. A(�3, 0) 5. B(2, �2) 6. C(1, 3)
For Questions 7 and 8, determine whether each transformation is a reflection, translation, dilation, or rotation.
7. 8.
9. Express the relation {(8, 7), (�2, 0), (1, 0), (4, �5), (�1, 3)} as a mapping. Then determine the domain and range.
10. Express the relation shown in the graph as a set of ordered pairs.Then write the inverse of the relation.
11. Find the solution set for 3x � y � 7,given the replacement set {(2, 1), (�3, �16), (5, 8), (4, �19)}.
12. Solve y � �2x � 1 if the domain is {�3, �2, �1, 0, 1}.Graph the solution set.
For Questions 13 and 14, determine whether each equation is a linear equation. If so, write the equation in standard form.
13. �1x� � �
1y� � �
23�
14. 4x � 2y
15. Graph the equation x � 4y � 3 � 0.
y
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NAME DATE PERIOD
SCORE 44
Ass
essm
ent
y
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P
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y
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7.
8.
9.
10.
11.
12.
13.
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© Glencoe/McGraw-Hill 270 Glencoe Algebra 1
Chapter 4 Test, Form 2D (continued)
Determine whether each relation is a function.
16. 17.
For Questions 18 and 19, if g(x) � x2 � 2x � 4, find each value.
18. g(�5) 19. g(t � 1)
20. Determine whether the sequence 7, 11, 15, 19, … is an arithmetic sequence. If so, state the common difference.
21. Find the next three terms of the arithmetic sequence �25, �22, �19, �16, … .
22. Write an equation for the nth term of the sequence 3, 12, 21, 30, … . Then graph the first five terms of the sequence.
23. Find the next two items in the pattern.
24. Use the table below that shows the amount of gasoline a car consumes for different distances driven.
Write an equation in function notation for the relationship between distance and gasoline used.
25. Joseph wants to reduce a rectangular photograph that is 3 inches wide and 5 inches tall by a scale factor of 2.5 so it will fit on his report. What will be the dimensions of the new photograph? Use a coordinate system to draw a photograph of the original rectangle and the reduced photograph. Place one corner of each photograph at the origin and for each photograph write the coordinates of the other three vertices.
Bonus Graph the points (4, �2), (4, 3), (�2, 3). Find a fourth point that completes a rectangle with the given three points, then graph the rectangle on the same coordinate plane.
...
y
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NAME DATE PERIOD
44
x y
�2 7
0 0
1 �2
1 3
Distance (mi) 1 2 3 4 5
Gasoline (gal) 0.05 0.10 0.15 0.20 0.25
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
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2 3 4 5 6 7
Chapter 4 Test, Form 3
© Glencoe/McGraw-Hill 271 Glencoe Algebra 1
1. Write the ordered pair that describes a point 8 units below the origin and on the y-axis.
2. Plot the points (�3, 1.5) and ��32�, �4� on a coordinate plane,
and label each point with the ordered pairs.
3. Determine whether a reflection, translation, dilation, or rotation is being shown.
4. Triangle MNP with M(1, 2), N(3, 4), and P(4, �1) is reflected over the y-axis, then translated 2 units right and 2 units down. Find the coordinates of the vertices after the given transformations are performed. Then, graph the preimage and its image.
5. Express the relation {(4, �1), (�2, 3), (�1, �2), (6, �2), (3, �1)} as a mapping. Then determine the domain and range.
6. Express the relation shown in the graph as a set of ordered pairs.Then write the inverse of the relation.
7. Find the solution set for 4x � 5y � 15,given the replacement set {(�10, �12), (�3, �5.4), (5, 1.2), (6, 3), (15, 9)}.
8. Solve the equation 7x � 2y � 8 if the domain is {�4, 3, 5, 6}. Graph the solution set.
9. Determine whether 3x � 4y � 7 � 3y � 1 is a linear equation. If so, write the equation in standard form.
NAME DATE PERIOD
SCORE 44
Ass
essm
ent
y
xO
1.
2.
3.
4.
5.
6.
7.
8.
9.
y
xO
X Y
y
xO
y
xO
© Glencoe/McGraw-Hill 272 Glencoe Algebra 1
Chapter 4 Test, Form 3 (continued)
10. Graph �23x� � �2
y� � 1.
Determine whether each relation is a function.
11. 3x � 11 12.
13. If f(x) � 3x2 � 4x, find �2[f(2p)].
14. Determine whether the sequence 0, �12�, 1, �
32�, … is an
arithmetic sequence. If it is, state the common difference.
15. Find the value of y that makes 9, 4, y, �6, … an arithmetic sequence.
16. Write an equation for the nth term of the arithmetic sequence �15, �11, �7, �3, … . Then graph the first five terms of the sequence.
17. Find the tenth figure in the pattern below.
For Questions 18 and 19, use the table below that shows the value of a vending machine over the first five years of use.
18. Write an equation in function notation for the relationship between years of use t and value v(t).
19. When will the value of the vending machine reach 0?
20. Brian collects baseball cards. His father gave him 20 cards to start his collection on his tenth birthday. Each year Brian adds about 15 cards to his collection. About how many years will it take to fill his collection binder if it holds 200 cards?
Bonus Solve the equation �2x
� � �3y
� � 10 if the domain is
{�4, �1, 2, 3, 6}. Then state the inverse of the solution set.
y
xO
NAME DATE PERIOD
44
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
an
n
y
xO
Number of years 1 2 3 4 5
Value (dollars) 1810 1620 1430 1240 1050
0
2000
Chapter 4 Open-Ended Assessment
© Glencoe/McGraw-Hill 273 Glencoe Algebra 1
Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solution in more thanone way or investigate beyond the requirements of the problem.
1. a. Give the coordinates of a point on the coordinate plane.Name the quadrant in which the point is located.
b. Reflect the point in part a across the y-axis and find thecoordinates of the image. Graph the preimage and its image.
c. Explain how the coordinates of a point can be determined tobe positive or negative by knowing in which quadrant thepoint is located.
2. a. List any two transformations and describe the differencesbetween the two transformations chosen.
b. Describe any similarities between the two transformationschosen for part a.
3. Use the set {�1, 0, 1, 2} as a domain and the set {�3, �1, 4, 5} asa range.a. Create a relation. Express the relation as a set of ordered
pairs. Then state the inverse of the relation.b. Create a relation that is not a function. Express the relation
as a table, a graph, and a mapping.c. Explain why the relation created for part b is not a function.
4. Write a linear equation in standard form. Then explain how tograph the equation.
5. An equation is written using the function notation f(x).Explain what f(2) represents and describe how to find f(2).
6. a. Write a sequence that is an arithmetic sequence. State thecommon difference, and find a6.
b. Write a sequence that is not an arithmetic sequence.Determine whether the sequence has a pattern, and if sodescribe the pattern.
c. Determine if the sequence 1, 1, 1, 1, … is an arithmeticsequence. Explain your reasoning.
NAME DATE PERIOD
SCORE 44
Ass
essm
ent
© Glencoe/McGraw-Hill 274 Glencoe Algebra 1
Chapter 4 Vocabulary Test/Review
Choose from the terms above to complete each sentence.
1. In mathematics, points are located in reference to two
perpendicular number lines called .
2. The axes in the coordinate plane intersect at a common zero
point called the .
3. The x-axis and y-axis separate the coordinate plane into four
regions called .
4. are movements of geometric figures.
5. In a(n) , a figure is slid horizontally,vertically, or both.
6. The of any relation is obtained byswitching the coordinates of each ordered pair of the relation.
7. For a(n) Ax � By � C, the numbersA, B, and C cannot all be zero.
8. A(n) is a relation in which eachelement of the domain is paired with exactly one element of therange.
9. The can be used to determine if agraph represents a function.
In your own words—Define each term.
10. coordinate plane
11. mapping
arithmetic sequenceaxescommon differencecoordinate planedilationequation in two variablesfunctionfunction notationgraph
imageinductive reasoninginverselinear equationlook for a patternmappingoriginpreimagequadrant
reflectionrotationsequencesolutionstandard formtermstransformationtranslationvertical line test
x-axisx-coordinatex-intercepty-axisy-coordinatey-intercept
NAME DATE PERIOD
SCORE 44
Chapter 4 Quiz (Lessons 4–1 and 4–2)
44
© Glencoe/McGraw-Hill 275 Glencoe Algebra 1
Write the ordered pair for each point shown. Name the quadrant in which the point is located.
1. P 2. T
For Questions 3 and 4, identify each transformation as a reflection,translation, dilation, or rotation.
3. 4.
5. Find the coordinates of the vertices of triangle ABC with A(1, 2), B(3, 3), and C(3, �1), after the triangle is reflected over the y-axis. Then graph the preimage and its image.
NAME DATE PERIOD
SCORE
Chapter 4 Quiz (Lessons 4–3 and 4–4)
1. Express the relation {(3, 5), (�4, 6), (3, 8), (2, 4), (1, 3)} as a mapping. Then determine the domain and range.
2. Express the relation shown in the graph as a set of ordered pairs.Then write the inverse of the relation.
3. Find the solution set for y � 4x � 3,given the replacement set {(�3, 9), (�2, �11), (0, �2), (2, 5)}.
4. Solve 3x � 2y � �6 if the domain is {�2, �1, 0, 2, 3}.
5. Solve the equation y � 2x � 4 if the domain is {�3, �2, �1, 0, 1}.
NAME DATE PERIOD
SCORE 44
Ass
essm
ent
y
xOP
T
y
xO
1.
2.
3.
4.
5.
y
xO
1.
2.
3.
4.
5.
X Y
© Glencoe/McGraw-Hill 276 Glencoe Algebra 1
1. Determine whether y � 2x � 1 is a linear equation.If so, write the equation in standard form.
2. Graph 3x � y � 3.
3. Determine whether the relation is a function.
4. If g(x) � x2 � 3x � 2, find g(�4). 4.
5. STANDARDIZED TEST PRACTICE If � x � x2 � 3x � 4,then � 6 �
A. �8. B. 22. C. 58. D. 14. 5.
Chapter 4 Quiz (Lessons 4–7 and 4–8)
1. Determine whether 2, 5, 9, 14, … is an arithmetic sequence. 1.If so, state the common difference.
2. Find the next three terms of the arithmetic sequence 2.5, 9, 13, 17, … .
3. Find the 15th term of the arithmetic sequence if 3.a1 � �3 and d � 2.
4. Find the next three terms in the sequence 4.3125, 625, 125, 25, … .
5. Write an equation in function 5.notation for the relation graphed.
y
xO
NAME DATE PERIOD
SCORE
Chapter 4 Quiz (Lessons 4–5 and 4–6)
44
44
1.
2.
3.
y
xO
NAME DATE PERIOD
SCORE
y
xO
Chapter 4 Mid-Chapter Test (Lessons 4–1 through 4–4)
© Glencoe/McGraw-Hill 277 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. Write the ordered pair for point P and name the quadrant in which it is located.A. (2, �3); II B. (2, �3); IIIC. (�2, �3); III D. (�2, �3); II 1.
2. Determine what type of transformation is shown.A. reflection B. translationC. dilation D. rotation 2.
3. What is the inverse of the relation {(�1, 2), (3, �4), (0, 5)}?A. {(2, �1), (�4, 3), (5, 0)} B. {(�2, 1), (4, �3), (�5, 0)}C. {(1, �2), (�3, 4), (0, �5)} D. {(1, 2), (�3, �4), (0, 5)} 3.
For Questions 4 and 5 use the following information.The total T charged by a phone company can be represented by the equation T � 30 � 0.10m where m is the number of minutes.
4. Solve the equation for m.
A. m � �0.T10� � 30 B. m � 0.1(T � 30) C. m � �0.
T10� � 30 D. m � �
T0�.10
30� 4.
5. Find the number of minutes if the total charge is $31.00.A. 100 B. 10 C. 1 D. 340 5.
6. Express the relation {(�3, �2), (3, �1), (5, �2), (7, 0)} 6.as a mapping.
7. For the triangle described below, find the coordinates of the 7.vertices of each figure after the given transformation is performed. Then graph the preimage and its image.Triangle DEF with D(�1, 1), E(�4, 1), and F(�2, 4) reflected over the y-axis
Solve each equation for the given domain.
8. y � 2x � 3 for x � {�2, �1, 0, 2, 3} 8.
9. 3y � x � 6 for x � {�3, 0, 3, 6} 9.
X Y
Part II
Part I
NAME DATE PERIOD
SCORE 44
Ass
essm
ent
y
xO
P
© Glencoe/McGraw-Hill 278 Glencoe Algebra 1
Chapter 4 Cumulative Review (Chapters 1–4)
1. Find the solution of y � �23� � �
2125�
if the replacement set is
��25�, �
35�, �
45�, 1, 1�
15��. (Lesson 1–3)
2. Simplify 5m � 8n � 3m � n. (Lesson 1–6)
3. The average longevity in years of 10 different farm animals is listed below. Make a stem-and-leaf plot. (Lesson 2–5)
12 12 12 15 12 8 20 10 5 12
4. Find �38�. Round to the nearest hundredth. (Lesson 2–7)
5. Translate the following equation into a verbal sentence.
�4x
� � y � �2��xy��
(Lesson 3–1)
6. Find the discounted price. clock: $15.00discount: 15% (Lesson 3–7)
7. Solve �7x � 23 � 37. (Lesson 3–4)
8. Use cross products to determine whether the ratios �47� and �1
151�
form a proportion. Write yes or no. (Lesson 3–6)
For Questions 9–11, use the graph.
9. Write the ordered pair for point A, and name the quadrant in which the point is located.(Lesson 4–1)
10. Express the relation as a set of ordered pairs. Then determine the domain and range. (Lesson 4–3)
11. Determine whether the relation is a function. (Lesson 4–6)
12. Find the coordinates of the vertices of triangle ABC withA(�1, 0), B(2, 4), and C(3, 1) reflected over the x-axis. Thengraph the preimage and its image. (Lesson 4–2)
13. Solve 4x � 5 � y if the domain is {�3, �1, 1, 2, 5}. (Lesson 4–4)
14. Graph 2x � 3y � 6. (Lesson 4–5)
y
xO
BE
C D
A
G
F
NAME DATE PERIOD
44
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14. y
xO
y
x
Standardized Test Practice (Chapters 1–4)
© Glencoe/McGraw-Hill 279 Glencoe Algebra 1
1. Which vehicle is a counterexample for the statement.If an automobile is a sports car, then it is red. (Lesson 1–7)
A. a red pick-up truck B. a white motor homeC. a red sports car D. a yellow sports car 1.
2. Dion owns a delivery service. He charges his customers $15.00 for each delivery. His expenses include $7000 for the motorcycle he drives and $0.42 for gasoline per trip. Which equation could Dion use to calculate his profit p for d deliveries? (Lesson 1–8)
E. p � 15 � 0.42d F. p � 14.58d � 7000G. p � 7000 � 15d H. p � 0.42d � 7000 2.
3. Evaluate �4xy if x � 5.3 and y � �0.4. (Lesson 2–3)
A. 9.7 B. �9.7 C. 8.48 D. �8.48 3.
4. Which measure of central tendency best represents the data? new car prices: $14,500, $12,400, $18,500, $12,400, $28,900,$19,100, $17,300, $22,900, $17,800, $21,600 (Lesson 2–5)
E. median F. mean G. mode H. none 4.
5. Translate the sentence into an equation. (Lesson 3–1)
Five times the sum of s and t is as much as four times r.A. 5s � t � 4 B. 5s � t � r C. 5(s � t) � 4r D. s � t � 5(4r) 5.
6. Solve 8(x � 5) � 12(4x � 1) � 12. (Lesson 3–5)
E. ��170�
F. ��57� G. �2 H. �1 6.
7. Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 miles per hour faster than Charlene.They meet in 5 hours. Find Charlene’s speed. (Lesson 3–9)
A. 34 mph B. 50 mph C. 40.4 mph D. 68 mph 7.
8. Determine which equation is a linear equation. (Lesson 4–5)
E. x2 � y � 4 F. x � y � 4 G. xy � 4 H. �1x� � y � 4 8.
9. If f(x) � 7 � 2x, find f(3) � 6. (Lesson 4–6)
A. 11 B. 7 C. 14 D. –11 9.
10. Chapa is beginning an exercise program that calls for 30 push-ups each day for the first week. Each week thereafter, she has to increase her push-ups by 2. Which week of her program will be the first one in which she will do 50 push-ups a day? (Lesson 4–7)
E. 9th week F. 10th week G. 11th week H. 12th week 10. HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
NAME DATE PERIOD
44
Ass
essm
ent
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
© Glencoe/McGraw-Hill 280 Glencoe Algebra 1
Standardized Test Practice (continued)
NAME DATE PERIOD
44
NAME DATE PERIOD
11. Evaluate 27 � � y � z � if y � �4.9 and z � �5.1. (Lesson 2–1)
12. The ratio of a to b is �47�. If a is 16, find the
value of b. (Lesson 3–6)
13. Tariq is enlarging a map by a scale factor of
3�12�. On his original map the distance from
his home to his school is 4 inches. How far in inches is this distance on the enlargement?(Lesson 4–2)
14. The equation C � �F
1�.8
32� relates the
temperature in degrees Fahrenheit F to degrees Celsius C. If the temperature is 25°C in Rome, Italy, what is the temperature in degrees Fahrenheit?(Lesson 4–4)
Column A Column B
15. 15.
(Lessons 2–3 and 2–4)
16. Given: x � 4 � 10 16.
(Lesson 3–2)
17. 17.
(Lesson 4–1)
DCBAthe quadrant in whichpoint (�2, 4) is located
the quadrant in whichpoint (�3, �1) is located
15x
DCBA
DCBA3(a � 2)�14 �
77a
�
Part 3: Quantitative Comparison
Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.
11. 12.
13. 14.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
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.
99 9 987654321
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0 0 0
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.
99 9 987654321
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87654321
87654321
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
A
D
C
B
Standardized Test PracticeStudent Record Sheet (Use with pages 252–253 of the Student Edition.)
© Glencoe/McGraw-Hill A1 Glencoe Algebra 1
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 9
Solve the problem and write your answer in the blank.
Also enter your answer by writing each number or symbol in a box.Then fill in the corresponding oval for that number or symbol.
10 (grid in) 10 13 14
11
12
13 (grid in)
14 (grid in)
15 (grid in) 15 16
16 (grid in)
Select the best answer from the choices given and fill in the corresponding oval.
17 18 19 20
Record your answers for Question 21 on the back of this paper.
DCBADCBADCBADCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
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0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
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87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
DCBADCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
44
An
swer
s
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Quantitative ComparisonPart 3 Quantitative Comparison
Part 4 Open-EndedPart 4 Open-Ended
Part 1 Multiple ChoicePart 1 Multiple Choice
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Th
e C
oo
rdin
ate
Pla
ne
NA
ME
____
____
____
____
____
____
____
____
____
____
____
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AT
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____
____
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IOD
____
_
4-1
4-1
©G
lenc
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3G
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Lesson 4-1
Iden
tify
Po
ints
In t
he d
iagr
am a
t th
e ri
ght,
poin
ts a
re
loca
ted
in r
efer
ence
to
two
perp
endi
cula
r nu
mbe
r li
nes
call
ed
axes
.The
hor
izon
tal n
umbe
r li
ne is
the
x-a
xis,
and
the
vert
ical
num
ber
line
is t
he y
-axi
s.T
he p
lane
con
tain
ing
the
x- a
nd y
-axe
s is
cal
led
the
coor
din
ate
pla
ne.
Poi
nts
in t
he c
oord
inat
e pl
ane
are
nam
ed b
y or
dere
d pa
irs
of t
he f
orm
(x,
y).T
he f
irst
num
ber,
or
x-co
ord
inat
eco
rres
pond
s to
a n
umbe
r on
the
x-a
xis.
The
sec
ond
num
ber,
or y
-coo
rdin
ate,
corr
espo
nds
to a
num
ber
on t
he y
-axi
s.
Th
e ax
es d
ivid
e th
e co
ordi
nat
e pl
ane
into
Qu
adra
nts
I,I
I,II
I,an
d IV
,as
show
n.T
he
poin
t w
her
e th
e ax
es i
nte
rsec
t is
cal
led
the
orig
in.T
he
orig
in h
as c
oord
inat
es (
0,0)
.
x
y
O
PQ
R
Quad
rant
III
Quad
rant
IIQu
adra
nt I
Quad
rant
IV
Wri
te a
n o
rder
edp
air
for
poi
nt
Rab
ove.
Th
e x-
coor
din
ate
is 0
an
d th
e y-
coor
din
ate
is 4
.Th
us
the
orde
red
pair
for
Ris
(0,
4).
Wri
te o
rder
ed p
airs
for
poi
nts
Pan
d Q
abov
e.T
hen
nam
e th
e q
uad
ran
t in
wh
ich
eac
h p
oin
t is
loc
ated
.
Th
e x-
coor
din
ate
of P
is �
3 an
d th
e y-
coor
din
ate
is�
2.T
hu
s th
e or
dere
d pa
ir f
or P
is (
�3,
�2)
.Pis
in
Qu
adra
nt
III.
Th
e x-
coor
din
ate
of Q
is 4
an
d th
e y-
coor
din
ate
is�
1.T
hu
s th
e or
dere
d pa
ir f
or Q
is (
4,�
1).Q
is i
nQ
uad
ran
t IV
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
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cises
Wri
te t
he
ord
ered
pai
r fo
r ea
ch p
oin
t sh
own
at
the
righ
t.N
ame
the
qu
adra
nt
in w
hic
h t
he
poi
nt
is l
ocat
ed.
1.N
(3,0
),n
on
e2.
P(�
2,�
3),I
II
3.Q
(0,5
),n
on
e4.
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3,4)
,II
5.S
(5,�
2),I
V6.
T(�
5,0)
,no
ne
7.U
(1,1
),I
8.V
(5,4
),I
9.W
(�2,
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I10
.Z(�
1,0)
,no
ne
11.A
(3,�
3),I
V12
.B(0
,�4)
,no
ne
13.W
rite
th
e or
dere
d pa
ir t
hat
des
crib
es a
poi
nt
4 u
nit
s do
wn
fro
m a
nd
3 u
nit
s to
th
e ri
ght
of t
he
orig
in.
(3,�
4)
14.W
rite
th
e or
dere
d pa
ir t
hat
is
8 u
nit
s to
th
e le
ft o
f th
e or
igin
an
d li
es o
n t
he
x-ax
is.
(�8,
0)
x
y O
P
QR
N
S
TU
V
W
Z
AB
©G
lenc
oe/M
cGra
w-H
ill21
4G
lenc
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lgeb
ra 1
Gra
ph
Po
ints
To
grap
han
ord
ered
pai
r m
ean
s to
dra
w a
dot
at
the
poin
t on
th
eco
ordi
nat
e pl
ane
that
cor
resp
onds
to
the
orde
red
pair
.To
grap
h a
n o
rder
ed p
air
(x,y
),be
gin
at t
he
orig
in.M
ove
left
or
righ
t x
un
its.
Fro
m t
her
e,m
ove
up
or d
own
yu
nit
s.D
raw
a d
ot a
tth
at p
oin
t.
Plo
t ea
ch p
oin
t on
a c
oord
inat
e p
lan
e.
a.R
(�3,
2)S
tart
at
the
orig
in.M
ove
left
3 u
nit
s si
nce
th
e x-
coor
din
ate
is �
3.M
ove
up
2 u
nit
s si
nce
th
e y-
coor
din
ate
is 2
.Dra
w a
do
t an
d la
bel
it R
.
b.
S(0
,�3)
Sta
rt a
t th
e or
igin
.Sin
ce t
he
x-co
ordi
nat
e is
0,t
he
poin
t w
ill
be l
ocat
ed o
n t
he
y-ax
is.M
ove
dow
n 3
un
its
sin
ce t
he
y-co
ordi
nat
e is
�3.
Dra
w a
dot
an
d la
bel
it S
.
Plo
t ea
ch p
oin
t on
th
e co
ord
inat
e p
lan
e at
th
e ri
ght.
1.A
(2,4
)2.
B(0
,�3)
1–16
.See
gra
ph
.
3.C
(�4,
�4)
4.D
(�2,
0)
5.E
(1,�
4)6.
F(0
,0)
7.G
(5,0
)8.
H(�
3,4)
9.I(
4,�
5)10
.J(�
2,�
2)
11.K
(2,�
1)12
.L(�
1,�
2)
13.M
(0,3
)14
.N(5
,�3)
15.P
(4,5
)16
.Q(�
5,2)
x
y
O
AM
N
P
Q
BC
D
E
FG
H
I
JK
L
x
y O
R
S
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Th
e C
oo
rdin
ate
Pla
ne
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-1
4-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 4-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Th
e C
oo
rdin
ate
Pla
ne
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-1
4-1
©G
lenc
oe/M
cGra
w-H
ill21
5G
lenc
oe A
lgeb
ra 1
Lesson 4-1
Wri
te t
he
ord
ered
pai
r fo
r ea
ch p
oin
t sh
own
at
the
righ
t.N
ame
the
qu
adra
nt
in w
hic
h t
he
poi
nt
is l
ocat
ed.
1.A
(�4,
�4)
;III
2.B
(3,2
);I
3.C
(2,�
1);
IV4.
D(�
3,4)
;II
5.E
(�2,
0);
no
ne
6.F
(4,�
3);
IV
Wri
te t
he
ord
ered
pai
r fo
r ea
ch p
oin
t sh
own
at
the
righ
t.N
ame
the
qu
adra
nt
in w
hic
h t
he
poi
nt
is l
ocat
ed.
7.G
(�2,
2);
II8.
H(1
,�1)
;IV
9.J
(3,4
);I
10.K
(�2,
�2)
;III
11.L
(1,3
);I
12.M
(0,�
4);
no
ne
Plo
t ea
ch p
oin
t on
th
e co
ord
inat
e p
lan
e at
th
e ri
ght.
13.M
(2,4
)14
.N(�
3,�
3)
15.P
(2,�
2)16
.Q(0
,3)
17.R
(4,1
)18
.S(�
4,1)
Plo
t ea
ch p
oin
t on
th
e co
ord
inat
e p
lan
e at
th
e ri
ght.
19.T
(4,0
)20
.U(�
3,2)
21.W
(�2,
�3)
22.X
(2,2
)
23.Y
(�3,
�2)
24.Z
(3,�
3)W
x
y
OT
XU
Y
Z
M
x
y
O
Q
S N
R
P
x
y
O
GJ
KHL
M
x
y
O
D
F
EC
B
A
©G
lenc
oe/M
cGra
w-H
ill21
6G
lenc
oe A
lgeb
ra 1
Wri
te t
he
ord
ered
pai
r fo
r ea
ch p
oin
t sh
own
at
the
righ
t.N
ame
the
qu
adra
nt
in w
hic
h t
he
poi
nt
is l
ocat
ed.
1.A
(0,�
1);
no
ne
2.B
(�5,
5);
II
3.C
(�5,
�2)
;III
4.D
(5,�
5);
IV
5.E
(3,3
);I
6.F
(�1,
1);
II
7.G
(2,�
3);
IV8.
H(�
1,�
4);
III
9.I
(�3,
0);
no
ne
10.J
(2,5
);I
11.K
(5,�
2);
IV12
.L(4
,2);
I
Plo
t ea
ch p
oin
t on
th
e co
ord
inat
e p
lan
e at
th
e ri
ght.
13.M
(�3,
3)14
.N(3
,�2)
15.P
(5,1
)
16.Q
(�4,
�3)
17.R
(0,5
)18
.S(�
1,�
2)
19.T
(�5,
1)20
.V(1
,�5)
21.W
(2,0
)
22.X
(�2,
�4)
23.Y
(4,4
)24
.Z(�
1,2)
25.C
HES
SL
ette
rs a
nd
nu
mbe
rs a
re u
sed
to s
how
th
e po
siti
ons
of c
hes
s pi
eces
an
d to
des
crib
e th
eir
mov
es.
For
exa
mpl
e,in
th
e di
agra
m a
t th
e ri
ght,
a w
hit
e pa
wn
is
loc
ated
at
f5.N
ame
the
posi
tion
s of
eac
h o
f th
ere
mai
nin
g ch
ess
piec
es.
wh
ite
paw
ns:
a7,c
6;b
lack
paw
ns:
b4,
d7;
wh
ite
kin
g:
g3;
bla
ck k
ing
:e8
AR
CH
AEO
LOG
YF
or E
xerc
ises
26
and
27,
use
th
e gr
id a
t th
e ri
ght
that
sh
ows
the
loca
tion
of
arro
wh
ead
s ex
cava
ted
at
a m
idd
en—
a p
lace
wh
ere
peo
ple
in
th
e p
ast
du
mp
ed
tras
h,f
ood
rem
ain
s,an
d o
ther
dis
card
ed i
tem
s.
26.W
rite
th
e co
ordi
nat
es o
f ea
ch a
rrow
hea
d.(1
,1),
(3,2
),(1
,4)
27.S
upp
ose
an a
rch
aeol
ogis
t di
scov
ers
two
oth
er a
rrow
hea
ds
loca
ted
at (
1,2)
an
d (3
,3).
Dra
w a
n a
rrow
hea
d at
eac
h o
f th
ese
loca
tion
s on
th
e gr
id.
01
2M
eter
s
Meters
34
4 3 2 1 0
8 7 6 5 4 3 2 1
King
Paw
n
ab
cd
ef
ghW
x
y
O
R
N
Y
T Q
Z
V
P
M
XS
x
y
O
C
JB
AK
DL
E
F
I
GH
Pra
ctic
e (
Ave
rag
e)
Th
e C
oo
rdin
ate
Pla
ne
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-1
4-1
Answers (Lesson 4-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csT
he
Co
ord
inat
e P
lan
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-1
4-1
©G
lenc
oe/M
cGra
w-H
ill21
7G
lenc
oe A
lgeb
ra 1
Lesson 4-1
Pre-
Act
ivit
yH
ow d
o ar
chae
olog
ists
use
coo
rdin
ate
syst
ems?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-1
at
the
top
of p
age
192
in y
our
text
book
.
Wh
at d
o th
e te
rms
grid
sys
tem
,gri
d,a
nd
coor
din
ate
syst
emm
ean
to
you
?S
ee s
tud
ents
’wo
rk.
Rea
din
g t
he
Less
on
1.U
se t
he
coor
din
ate
plan
e sh
own
at
the
righ
t.
a.L
abel
th
e or
igin
O.
b.
Lab
el t
he
y-ax
is y
.
c.L
abel
th
e x-
axis
x.
2.E
xpla
in w
hy
the
coor
din
ates
of
the
orig
in a
re (
0,0)
.S
amp
le a
nsw
er:T
he
ori
gin
is t
he
inte
rsec
tio
n o
f tw
o n
um
ber
lin
es a
t th
eir
com
mo
n z
ero
po
int.
3.U
se t
he
orde
red
pair
(�
2,3)
.
a.E
xpla
in h
ow t
o id
enti
fy t
he
x- a
nd
y-co
ordi
nat
es.
Th
e x-
coo
rdin
ate
is t
he
firs
tn
um
ber
,th
e y-
coo
rdin
ate
is t
he
seco
nd
nu
mb
er.
b.
Nam
e th
e x-
an
d y-
coor
din
ates
.T
he
x-co
ord
inat
e is
�2,
the
y-co
ord
inat
e is
3.
c.D
escr
ibe
the
step
s yo
u w
ould
use
to
loca
te t
he
poin
t fo
r (�
2,3)
on
th
e co
ordi
nat
epl
ane.
Sta
rt a
t th
e o
rig
in.M
ove
left
2 u
nit
s.T
hen
mov
e u
p 3
un
its.
4.W
hat
doe
s th
e te
rm q
uad
ran
tm
ean
?S
amp
le a
nsw
er:
on
e o
f th
e fo
ur
reg
ion
s in
the
coo
rdin
ate
pla
ne
Hel
pin
g Y
ou
Rem
emb
er
5.E
xpla
in h
ow t
he
way
th
e ax
es a
re l
abel
ed o
n t
he
coor
din
ate
plan
e ca
n h
elp
you
rem
embe
r h
ow t
o pl
ot t
he
poin
t fo
r an
ord
ered
pai
r.S
amp
le a
nsw
er:T
he
rig
ht
sid
e o
f th
e h
ori
zon
tal a
xis
is la
bel
ed w
ith
th
e le
tter
x.T
his
is t
he
sid
e o
fth
e h
ori
zon
tal n
um
ber
lin
e w
her
e yo
u f
ind
po
siti
ve n
um
ber
s.T
he
top
en
do
f th
e ve
rtic
al n
um
ber
lin
e is
lab
eled
wit
h t
he
lett
er y
.Th
is is
th
e p
art
of
the
vert
ical
nu
mb
er li
ne
wh
ere
you
fin
d p
osi
tive
nu
mb
ers.
x
y
O
©G
lenc
oe/M
cGra
w-H
ill21
8G
lenc
oe A
lgeb
ra 1
Mid
po
int
Th
e m
idpo
int
of a
lin
e se
gmen
t is
th
e po
int
that
lie
s ex
actl
y h
alfw
aybe
twee
n t
he
two
endp
oin
ts o
f th
e se
gmen
t.T
he
coor
din
ates
of
the
mid
poin
t of
a l
ine
segm
ent
wh
ose
endp
oin
ts a
re (
x 1,y
1) a
nd
(x2,
y 2)
are
give
n b
y �
,�.
Fin
d t
he
mid
poi
nt
of e
ach
lin
e se
gmen
t w
ith
th
e gi
ven
en
dp
oin
ts.
1.(7
,1)
and
(�3,
1)2.
(5,�
2) a
nd
(9,�
8)
(2,1
)(7
,�5)
3.(�
4,4)
an
d (4
,�4)
4.(�
3,�
6) a
nd
(�10
,�15
)
(0,0
)(�
6.5,
�10
.5)
Plo
t ea
ch s
egm
ent
in t
he
coor
din
ate
pla
ne.
Th
en f
ind
th
e co
ord
inat
es o
f th
em
idp
oin
t.
5.J �K�
wit
h J
(5,2
) an
d K
(�2,
�4)
6.P�
Q�w
ith
P(�
1,4)
an
d Q
(3,�
1)
(1.5
,�1)
(1,1
.5)
You
are
giv
en t
he
coor
din
ates
of
one
end
poi
nt
of a
lin
e se
gmen
t an
d t
he
mid
poi
nt
M.F
ind
th
e co
ord
inat
es o
f th
e ot
her
en
dp
oin
t.
7.A
(�10
,3)
and
M(�
6,7)
8.D
(�1,
4) a
nd
M(3
,�6)
(�2,
11)
(7,�
16)
(3, –
1)
(–1,
4)
(1, 1
.5)
x
y
O
P
Q
(5, 2
)
(–2,
–4)
(1.5
, –1)
x
y
O
K
J
y 1�
y 2�
2x 1
�x 2
�2
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-1
4-1
Answers (Lesson 4-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Tran
sfo
rmat
ion
s o
n t
he
Co
ord
inat
e P
lan
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-2
4-2
©G
lenc
oe/M
cGra
w-H
ill21
9G
lenc
oe A
lgeb
ra 1
Lesson 4-2
Tran
sfo
rm F
igu
res
Tra
nsf
orm
atio
ns
are
mov
emen
ts o
f ge
omet
ric
figu
res.
Th
ep
reim
age
is t
he
posi
tion
of
the
figu
re b
efor
e th
e tr
ansf
orm
atio
n,a
nd
the
imag
eis
th
epo
siti
on o
f th
e fi
gure
aft
er t
he
tran
sfor
mat
ion
.
Ref
lect
ion
Afig
ure
is f
lippe
d ov
er a
line
.
Tran
slat
ion
Afig
ure
is s
lid h
oriz
onta
lly,
vert
ical
ly,
or b
oth.
Dila
tio
nA
figur
e is
enl
arge
d or
red
uced
.
Ro
tati
on
Afig
ure
is t
urne
d ar
ound
a p
oint
.
Det
erm
ine
wh
eth
er e
ach
tra
nsf
orm
atio
n i
s a
refl
ecti
on,t
ran
sla
tion
,d
ila
tion
,or
rota
tion
.
a.T
he
figu
re h
as b
een
fli
pped
ove
r a
lin
e,so
th
is i
s a
refl
ecti
on.
b.
Th
e fi
gure
has
bee
n t
urn
ed a
rou
nd
a po
int,
so t
his
is
a ro
tati
on.
c.T
he
figu
re h
as b
een
red
uce
d in
siz
e,so
th
is i
s a
dila
tion
.
d.
Th
e fi
gure
has
bee
n s
hif
ted
hor
izon
tall
y to
th
e ri
ght,
so t
his
is
atr
ansl
atio
n.
Det
erm
ine
wh
eth
er e
ach
tra
nsf
orm
atio
n i
s a
refl
ecti
on,t
ran
sla
tion
,dil
ati
on,o
rro
tati
on.
1.re
flec
tio
n2.
dila
tio
n
3.ro
tati
on
4.tr
ansl
atio
n
5.d
ilati
on
6.ro
tati
on
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill22
0G
lenc
oe A
lgeb
ra 1
Tran
sfo
rm F
igu
res
on
th
e C
oo
rdin
ate
Plan
eYo
u c
an p
erfo
rm t
ran
sfor
mat
ion
son
a c
oord
inat
e pl
ane
by c
han
gin
g th
e co
ordi
nat
es o
f ea
ch v
erte
x.T
he
vert
ices
of
the
imag
eof
th
e tr
ansf
orm
ed f
igu
re a
re i
ndi
cate
d by
th
e sy
mbo
l �,
wh
ich
is
read
pri
me.
Ref
lect
ion
ove
r x-
axis
(x,
y)
→(x
, �
y)
Ref
lect
ion
ove
r y-
axis
(x,
y)
→(�
x, y
)
Tran
slat
ion
(x,
y)
→(x
�a,
y�
b)
Dila
tio
n(x
, y
) →
(kx,
ky
)
Ro
tati
on
90�
cou
nte
rclo
ckw
ise
(x,
y)
→(�
y, x
)
Ro
tati
on
180
�(x
, y
) →
(�x,
�y
)
A t
rian
gle
has
ver
tice
s A
(�1,
1),B
(2,4
),an
d C
(3,0
).F
ind
th
eco
ord
inat
es o
f th
e ve
rtic
es o
f ea
ch i
mag
e b
elow
.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Tran
sfo
rmat
ion
s o
n t
he
Co
ord
inat
e P
lan
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-2
4-2
Exam
ple
Exam
ple
a.re
flec
tion
ove
r th
e x-
axis
To
refl
ect
a po
int
over
th
e x-
axis
,m
ult
iply
th
e y-
coor
din
ate
by �
1.
A(�
1,1)
→A
�(�
1,�
1)B
(2,4
) →
B�(
2,�
4)C
(3,0
) →
C�(
3,0)
Th
e co
ordi
nat
es o
f th
e im
age
vert
ices
are
A�(
�1,
�1)
,B�(
2,�
4),a
nd
C�(
3,0)
.
b.
dil
atio
n w
ith
a s
cale
fac
tor
of 2
Fin
d th
e co
ordi
nat
es o
f th
e di
late
d fi
gure
by m
ult
iply
ing
the
coor
din
ates
by
2.
A(�
1,1)
→A
�(�
2,2)
B(2
,4)
→B
�(4,
8)C
(3,0
) →
C�(
6,0)
Th
e co
ordi
nat
es o
f th
e im
age
vert
ices
are
A�(
�2,
2),B
�(4,
8),a
nd
C�(
6,0)
.
Exer
cises
Exer
cises
Fin
d t
he
coor
din
ates
of
the
vert
ices
of
each
fig
ure
aft
er t
he
give
n t
ran
sfor
mat
ion
is p
erfo
rmed
.
1.tr
ian
gle
RS
Tw
ith
R(�
2,4)
,S(2
,0),
T(�
1,�
1) r
efle
cted
ove
r th
e y-
axis
R�(
2,4)
,S�(
�2,
0),T
�(1,
�1)
2.tr
ian
gle
AB
Cw
ith
A(0
,0),
B(2
,4),
C(3
,0)
rota
ted
abou
t th
e or
igin
180
°A
�(0,
0),B
�(�
2,�
4),C
�(�
3,0)
3.pa
rall
elog
ram
AB
CD
wit
h A
(�3,
0),B
(�2,
3),C
(3,3
),D
(2,0
) tr
ansl
ated
3 u
nit
s do
wn
A�(
�3,
�3)
,B�(
�2,
0),C
�(3,
0),D
�(2,
�3)
4.qu
adri
late
ral
RS
TU
wit
h R
(�2,
2),S
(2,4
),T
(4,4
),U
(4,0
) di
late
d by
a f
acto
r of
R
�(�
1,1)
,S�(
1,2)
,T�(
2,2)
,U�(
2,0)
5.tr
ian
gle
AB
Cw
ith
A(�
4,0)
,B(�
2,3)
,C(0
,0)
rota
ted
cou
nte
rclo
ckw
ise
90°
A�(
0,�
4),B
�(�
3,�
2),C
�(0,
0)
6.h
exag
on A
BC
DE
Fw
ith
A(0
,0),
B(�
2,3)
,C(0
,4),
D(3
,4),
E(4
,2),
F(3
,0)
tran
slat
ed
2 u
nit
s u
p an
d 1
un
it t
o th
e le
ftA
�(�
1,2)
,B�(
�3,
5),C
�(�
1,6)
,D�(
2,6)
,E�(
3,4)
,F�(
2,2)
1 � 2
Answers (Lesson 4-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
Tran
sfo
rmat
ion
s o
n t
he
Co
ord
inat
e P
lan
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-2
4-2
©G
lenc
oe/M
cGra
w-H
ill22
1G
lenc
oe A
lgeb
ra 1
Lesson 4-2
Iden
tify
eac
h t
ran
sfor
mat
ion
as
a re
flec
tion
,tra
nsl
ati
on,d
ila
tion
,or
rota
tion
.
1.2.
3.
rota
tio
nre
flec
tio
ntr
ansl
atio
n
4.5.
6.
dila
tio
nre
flec
tio
nro
tati
on
For
Exe
rcis
es 7
–10,
com
ple
te p
arts
a a
nd
b.
a.F
ind
th
e co
ord
inat
es o
f th
e ve
rtic
es o
f ea
ch f
igu
re a
fter
th
e gi
ven
tran
sfor
mat
ion
is
per
form
ed.
b.
Gra
ph
th
e p
reim
age
and
its
im
age.
7.tr
ian
gle
AB
Cw
ith
A(1
,2),
B(4
,�1)
,an
d 8.
para
llel
ogra
m P
QR
Sw
ith
P(�
2,�
1),
C(1
,�1)
ref
lect
ed o
ver
the
y-ax
isQ
(3,�
1),R
(2,�
3),a
nd
S(�
3,�
3)
A�(
�1,
2),B
�(�
4,�
1),a
nd
tr
ansl
ated
3 u
nit
s u
pP
�(�
2,2)
,C
�(�
1,�
1)Q
�(3,
2),R
�(2,
0),a
nd
S�(
�3,
0)
9.tr
apez
oid
JK
LM
wit
h J
(�2,
1),K
(2,1
),10
.tri
angl
e S
TU
wit
h S
(3,3
),T
(5,1
),an
d L
(1,�
1),a
nd
M(�
1,�
1) d
ilat
ed b
y a
U(1
,1)
rota
ted
90°
cou
nte
rclo
ckw
ise
scal
e fa
ctor
of
2J
�(�
4,2)
,K�(
4,2)
,ab
out
the
orig
inL
�(2,
�2)
,an
d M
�(�
2,�
2)S
�(�
3,3)
,T�(
�1,
5),U
�(�
1,1)
S�
T�
U�
S
TU
x
y
O
J�J
K�
K L �L
M�M
x
y
O
P�
Q�
R�
S�
PQ
RS
x
y
O
A�
B�
C�
A
BC
x
y
O
©G
lenc
oe/M
cGra
w-H
ill22
2G
lenc
oe A
lgeb
ra 1
Iden
tify
eac
h t
ran
sfor
mat
ion
as
a re
flec
tion
,tra
nsl
ati
on,d
ila
tion
,or
rota
tion
.
1.2.
3.
refl
ecti
on
tran
slat
ion
rota
tio
n
For
Exe
rcis
es 4
–6,c
omp
lete
par
ts a
an
d b
.a.
Fin
d t
he
coor
din
ates
of
the
vert
ices
of
each
fig
ure
aft
er t
he
give
ntr
ansf
orm
atio
n i
s p
erfo
rmed
.b
.G
rap
h t
he
pre
imag
e an
d i
ts i
mag
e.
4.tr
ian
gle
DE
Fw
ith
D(2
,3),
5.tr
apez
oid
EF
GH
wit
h
6.tr
ian
gle
XY
Zw
ith
X(3
,1),
E(4
,1),
and
F(1
,�1)
E
(3,2
),F
(3,�
3),
Y(4
,�2)
,an
d Z
(1,�
3)
tran
slat
ed 4
un
its
left
G
(1,�
2),a
nd
H(1
,1)
ro
tate
d 90
°co
unte
rclo
ckw
ise
and
3 u
nit
s do
wn
refl
ecte
d ov
er t
he
y-ax
isab
out
the
orig
in
D�(
�2,
0),E
�(0,
�2)
,E
�(�
3,2)
,F�(
�3,
�3)
,X
�(�
1,3)
,F
�(�
3,�
4)G
�(�
1,�
2),H
�(�
1,1)
Y�(
2,4)
,Z�(
3,1)
GR
APH
ICS
For
Exe
rcis
es 7
–9,u
se t
he
dia
gram
at
the
righ
t
and
th
e fo
llow
ing
info
rmat
ion
.
A d
esig
ner
wan
ts t
o di
late
th
e ro
cket
by
a sc
ale
fact
or o
f ,a
nd
then
tra
nsl
ate
it 5
un
its
up.
7.W
rite
th
e co
ordi
nat
es f
or t
he
vert
ices
of
the
rock
et.
A(0
,�2)
,B(1
,�3)
,C(1
,�5)
,D(2
,�6)
,E(�
2,�
6),
F(�
1,�
5),G
(�1,
�3)
8.F
ind
the
coor
din
ates
of
the
fin
al p
osit
ion
of
the
rock
et.
A� �0
,4�,B
� �,4
�,C� �
,3�,D
� �1,2
�,E� ��
1,2
�,F� ��
,3�,G
� ��,4
�9.
Gra
ph t
he
imag
e on
th
e co
ordi
nat
e pl
ane.
10.D
ESIG
NR
amon
a tr
ansf
orm
ed f
igu
re A
BC
DE
Fto
des
ign
a
patt
ern
for
a q
uil
t.N
ame
two
diff
eren
t se
ts o
f tr
ansf
orm
atio
ns
she
cou
ld h
ave
use
d to
des
ign
th
e pa
tter
n. S
amp
le a
nsw
er:
refl
ecti
on
ove
r th
e x-
axis
,90�
cou
nte
rclo
ckw
ise
rota
tio
n,a
nd
th
en r
efle
ctio
n o
ver
the
y-ax
is;
thre
e 90
�co
un
terc
lock
wis
e ro
tati
on
s
AB C
DEF
x
y
O
1 � 21 � 2
1 � 21 � 2
1 � 21 � 2
1 � 2
1 � 2
1 � 2
AB C
DE
FG
x
y
O
y
O
X�
Y�
Z�
X
YZ
x
E�
F�
G�
H�
E FGH
x
y
OD
�
E�
F�
D
E
Fx
y
OPra
ctic
e (
Ave
rag
e)
Tran
sfo
rmat
ion
s o
n t
he
Co
ord
inat
e P
lan
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-2
4-2
Answers (Lesson 4-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csTr
ansf
orm
atio
ns
on
th
e C
oo
rdin
ate
Pla
ne
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-2
4-2
©G
lenc
oe/M
cGra
w-H
ill22
3G
lenc
oe A
lgeb
ra 1
Lesson 4-2
Pre-
Act
ivit
yH
ow a
re t
ran
sfor
mat
ion
s u
sed
in
com
pu
ter
grap
hic
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-2
at
the
top
of p
age
197
in y
our
text
book
.
In t
he
sen
ten
ce,“
Com
pute
r gr
aph
ic d
esig
ner
s ca
n c
reat
e m
ovem
ent
that
mim
ics
real
-lif
e si
tuat
ion
s,”
wh
at p
hra
se i
ndi
cate
s th
e u
se o
ftr
ansf
orm
atio
ns?
crea
te m
ovem
ent
Rea
din
g t
he
Less
on
1.S
upp
ose
you
loo
k at
a d
iagr
am t
hat
sh
ows
two
figu
res
AB
CD
Ean
d A
�B�C
�D�E
�.If
on
efi
gure
was
obt
ain
ed f
rom
th
e ot
her
by
usi
ng
a tr
ansf
orm
atio
n,h
ow d
o yo
u t
ell
wh
ich
was
the
orig
inal
fig
ure
?T
he
lett
ers
that
hav
e n
o p
rim
e sy
mb
ols
are
use
d f
or
vert
ices
of
the
ori
gin
al f
igu
re.
2.W
rite
th
e le
tter
of
the
term
an
d th
e R
oman
nu
mer
al o
f th
e fi
gure
th
at b
est
mat
ches
eac
hst
atem
ent.
a.A
fig
ure
is
flip
ped
over
a l
ine.
A.
dila
tion
I.
b.
A f
igu
re i
s tu
rned
aro
un
d a
poin
t.B
.tr
ansl
atio
nII
.
c.A
fig
ure
is
enla
rged
or
redu
ced.
C.
refl
ecti
onII
I.
d.
A f
igu
re i
s sl
id h
oriz
onta
lly,
vert
ical
ly,
D.
rota
tion
IV.
or b
oth
.
Hel
pin
g Y
ou
Rem
emb
er
3.G
ive
exam
ples
of
thin
gs i
n e
very
day
life
th
at c
an h
elp
you
rem
embe
r w
hat
ref
lect
ion
s,di
lati
ons,
and
rota
tion
s ar
e.S
amp
le a
nsw
er:
Fo
r a
refl
ecti
on
,th
ink
of
loo
kin
gat
yo
urs
elf
in a
mir
ror.
Fo
r a
dila
tio
n,t
hin
k o
f h
ow
yo
ur
han
d lo
oks
if y
ou
ho
ld it
far
fro
m y
ou
r fa
ce a
nd
th
en m
ove
it s
trai
gh
t in
,ver
y cl
ose
to
yo
ur
face
.Fo
r a
rota
tio
n,t
hin
k o
f tw
isti
ng
th
e to
p o
f a
jar
to o
pen
th
e ja
r.
B,I
V
A,I
I
D,I
II
C,I
©G
lenc
oe/M
cGra
w-H
ill22
4G
lenc
oe A
lgeb
ra 1
Th
e L
egen
dar
y C
ity
of
Ur
The
cit
y of
Ur
was
fou
nded
mor
e th
an f
ive
thou
sand
yea
rs a
go i
nM
esop
otam
ia (
mod
ern-
day
Iraq
).It
was
one
of
the
wor
ld’s
fir
st c
itie
s.B
etw
een
1922
and
193
4,ar
cheo
logi
sts
disc
over
ed m
any
trea
sure
s fr
omth
is a
ncie
nt c
ity.
A l
arge
cem
eter
y fr
om t
he 2
6th
cent
ury
B.C
.was
foun
d to
con
tain
lar
ge q
uant
itie
s of
gol
d,si
lver
,bro
nze,
and
jew
els.
The
man
y cu
ltur
al a
rtif
acts
tha
t w
ere
foun
d,su
ch a
s m
usic
al i
nstr
umen
ts,
wea
pons
,mos
aics
,and
sta
tues
,hav
e pr
ovid
ed h
isto
rian
s w
ith
valu
able
clue
s ab
out
the
civi
liza
tion
tha
t ex
iste
d in
ear
ly M
esop
otam
ia.
1.S
upp
ose
that
th
e or
dere
d pa
irs
belo
w r
epre
sen
t th
e vo
lum
e (c
m3 )
an
d m
ass
(gra
ms)
of
ten
art
ifac
ts f
rom
th
e ci
ty o
f U
r.P
lot
each
poi
nt
on t
he
grap
h.
A(1
0,15
0)
B(1
50,1
350)
C
(200
,176
0)
D(5
0,52
5)
E(1
00,1
500)
F
(10,
88)
G(2
00,2
100)
H
(150
,167
5)
I(10
0,90
0)
J(5
0,44
0)
2.T
he
equ
atio
n r
elat
ing
mas
s,de
nsi
ty,a
nd
volu
me
for
silv
er i
s m
�10
.5V
.Wh
ich
of
the
poin
ts i
n E
xerc
ise
1 ar
e so
luti
ons
for
this
equ
atio
n?
Dan
d G
3.S
upp
ose
that
th
e eq
uat
ion
m�
8.8V
rela
tes
mas
s,de
nsi
ty,a
nd
volu
me
for
the
kin
d of
bro
nze
use
d in
th
e an
cien
t ci
ty o
f U
r.W
hic
hof
th
e po
ints
in
Exe
rcis
e 1
are
solu
tion
s fo
r th
is e
quat
ion
?
C,F
,J
4.E
xpla
in w
hy
the
grap
h i
n E
xerc
ise
1 sh
ows
only
qu
adra
nt
1.
Nei
ther
th
e m
ass
no
r th
e vo
lum
e ca
n b
e a
neg
ativ
e n
um
ber
.
AF
JD
I
EB
HC
G
Vo
lum
e (c
m3 )
Mass (grams)
050
100
150
200
2400
2200
2000
1800
1600
1400
1200
1000 800
600
400
200
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-2
4-2
Answers (Lesson 4-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-3
4-3
©G
lenc
oe/M
cGra
w-H
ill22
5G
lenc
oe A
lgeb
ra 1
Lesson 4-3
Rep
rese
nt
Rel
atio
ns
A r
elat
ion
is a
set
of
orde
red
pair
s.A
rel
atio
n c
an b
ere
pres
ente
d by
a s
et o
f or
dere
d pa
irs,
a ta
ble,
a gr
aph
,or
a m
app
ing.
A m
appi
ng
illu
stra
tes
how
eac
h e
lem
ent
of t
he
dom
ain
is
pair
ed w
ith
an
ele
men
t in
th
e ra
nge
.
Exp
ress
th
e re
lati
on{(
1,1)
,(0,
2),(
3,�
2)}
as a
tab
le,a
grap
h,a
nd
a m
app
ing.
Sta
te t
he
dom
ain
an
d r
ange
of
the
rela
tion
.
Th
e do
mai
n f
or t
his
rel
atio
n i
s {0
,1,3
}.T
he
ran
ge f
or t
his
rel
atio
n i
s {�
2,1,
2}.
XY
1 0 3
1 2�
2
x
y O
xy
11
02
3�
2
A p
erso
n p
layi
ng
racq
uet
bal
l u
ses
4 ca
lori
es p
er h
our
for
ever
y p
oun
d h
e or
sh
e w
eigh
s.
a.M
ake
a ta
ble
to
show
th
e re
lati
on b
etw
een
wei
ght
and
cal
orie
s b
urn
ed i
n o
ne
hou
r fo
r p
eop
le w
eigh
ing
100,
110,
120,
and
130
pou
nd
s.So
urce
: The
Mat
h Te
ache
r’s B
ook
of L
ists
b.
Giv
e th
e d
omai
n a
nd
ran
ge.
dom
ain
:{10
0,11
0,12
0,13
0}ra
nge
:{40
0,44
0,48
0,52
0}c.
Gra
ph
th
e re
lati
on.
Wei
gh
t (p
ou
nd
s)Calories
100
120
0
520
480
440
400
x
y
xy
100
400
110
440
120
480
130
520
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
1.E
xpre
ss t
he
rela
tion
{(�
2,�
1),(
3,3)
,(4,
3)}
as
a ta
ble,
a gr
aph
,an
d a
map
pin
g.T
hen
det
erm
ine
the
dom
ain
an
d ra
nge
.d
om
ain
:{�
2,3,
4};
ran
ge:
{�1,
3}
2.T
he
tem
pera
ture
in
a h
ouse
dro
ps 2
°fo
r ev
ery
hou
r th
e ai
r co
ndi
tion
er i
s on
bet
wee
n t
he
hou
rs o
f 6
A.M
.an
d 11
A.M
.M
ake
a gr
aph
to
show
th
e re
lati
onsh
ip b
etw
een
tim
e an
dte
mpe
ratu
re i
f th
e te
mpe
ratu
re a
t 6
A.M
.was
82°
F.
Tim
e (A
.M.)
Temperature (�F)
68
79
1011
120
86 84 82 80 78 76 74 72
x
y
O
XY
�2 3 4
�1 3
xy
�2
�1
33
43
©G
lenc
oe/M
cGra
w-H
ill22
6G
lenc
oe A
lgeb
ra 1
Inve
rse
Rel
atio
ns
Th
e in
vers
eof
an
y re
lati
on i
s ob
tain
ed b
y sw
itch
ing
the
coor
din
ates
in e
ach
ord
ered
pai
r.
Exp
ress
th
e re
lati
on s
how
n i
n t
he
map
pin
g as
a s
et o
f or
der
edp
airs
.Th
en w
rite
th
e in
vers
e of
th
e re
lati
on.
Rel
atio
n:{
(6,5
),(2
,3),
(1,4
),(0
,3)}
Inve
rse:
{(5,
6),(
3,2)
,(4,
1),(
3,0)
}
Exp
ress
th
e re
lati
on s
how
n i
n e
ach
tab
le,m
app
ing,
or g
rap
h a
s a
set
of o
rder
edp
airs
.Th
en w
rite
th
e in
vers
e of
eac
h r
elat
ion
.
1.2.
{(�
2,4)
,(�
1,3)
,(2,
1),(
4,5)
};{(
�1,
0),(
2,�
8),(
4,�
1),(
5,2)
};{(
4,�
2),(
3,�
1),(
1,2)
,(5,
4)}
{(0,
�1)
,(�
8,2)
,(�
1,4)
,(2,
5)}
3.4.
{(�
3,5)
,(�
2,�
1),(
1,0)
,(2,
4)};
{(�
2,�
1),(
0,4)
,(1,
6),(
4,7)
};{(
5,�
3),(
�1,
�2)
,(0,
1),(
4,2)
}{(
�1,
�2)
,(4,
0),(
6,1)
,(7,
4)}
5.6.
{(�
2,2)
,(1,
�2)
,(2,
4),(
3,0)
};{(
�4,
0),(
�1,
�1)
,(0,
�2)
,(2,
1),(
4,3)
};{(
2,�
2),(
�2,
1),(
4,2)
,(0,
3)}
{(0,
�4)
,(�
1,�
1),(
�2,
0),(
1,2)
,(3,
4)}
x
y
Ox
y
O
XY
�2 0 1 4
�1 4 6 7
xy
�3
5
�2
�1
10
24
XY
�1 2 4 5
�8
�1 0 2
xy
�2
4
�1
3
21
45
XY
6 2 1 0
3 4 5
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-3
4-3
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 4-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-3
4-3
©G
lenc
oe/M
cGra
w-H
ill22
7G
lenc
oe A
lgeb
ra 1
Lesson 4-3
Exp
ress
eac
h r
elat
ion
as
a ta
ble
,a g
rap
h,a
nd
a m
app
ing.
Th
en d
eter
min
e th
ed
omai
n a
nd
ran
ge.
1.{(
�1,
�1)
,(1,
1),(
2,1)
,(3,
2)}
D �
{�1,
1,2,
3};
R �
{�1,
1,2}
2.{(
0,4)
,(�
4,�
4),(
�2,
3),(
4,0)
}
D �
{�4,
�2,
0,4}
;R
�{�
4,0,
3,4}
3.{(
3,�
2),(
1,0)
,(�
2,4)
,(3,
1)}
D �
{�2,
1,3}
;R
�{�
2,0,
1,4}
Exp
ress
th
e re
lati
on s
how
n i
n e
ach
tab
le,m
app
ing,
or g
rap
h a
s a
set
of o
rder
edp
airs
.Th
en w
rite
th
e in
vers
e of
th
e re
lati
on.
4.5.
6.
{(3,
�5)
,(�
4,3)
,(7,
6),
{(9,
7),(
�5,
6),(
4,8)
,{(
�3,
1),(
�3,
2),(
3,1)
,(1
,�2)
};{(
�5,
3),
(4,2
)};
{(7,
9),
(3,�
3)};
{(1,
�3)
,(3
,�4)
,(6,
7),(
�2,
1)}
(6,�
5),(
8,4)
,(2,
4)}
(2,�
3),(
1,3)
,(�
3,3)
}
x
y
O
XY
9�
5 4
7 6 8 2
xy
3�
5
�4
3
76
1�
2
XY
3 1�
2
�2 0 4 1
x
y
O
xy
3�
2
10
�2
4
3 1
XY
0�
4�
2 4
4�
4 3 0x
y
O
xy
04
�4
�4
�2
3
40
XY
�1 1 2 3
�1 1 2
x
y
O
xy
�1
�1
11
21
3 2
©G
lenc
oe/M
cGra
w-H
ill22
8G
lenc
oe A
lgeb
ra 1
Exp
ress
eac
h r
elat
ion
as
a ta
ble
,a g
rap
h,a
nd
a m
app
ing.
Th
en d
eter
min
e th
ed
omai
n a
nd
ran
ge.
1.{(
4,3)
,(�
1,4)
,(3,
�2)
,(2,
3),(
�2,
1)}
D �
{�2,
�1,
2,3,
4};
R �
{�2,
1,3,
4}
Exp
ress
th
e re
lati
on s
how
n i
n e
ach
tab
le,m
app
ing,
or g
rap
h a
s a
set
of o
rder
edp
airs
.Th
en w
rite
th
e in
vers
e of
th
e re
lati
on.
2.3.
4.
{(0,
9),(
�8,
3),
{(9,
5),(
9,3)
,(�
6,�
5),
{(�
3,�
1),(
�2,
�2)
,(2
,�6)
,(1,
4)};
(4,3
),(8
,�5)
,(8,
7)};
(�1,
�3)
,(1,
1),(
2,1)
,{(
9,0)
,(3,
�8)
,{(
5,9)
,(3,
9),(
�5,
�6)
,(3
,1)}
;{(�
1,�
3),(
�2,
�2)
,(�
6,2)
,(4,
1)}
(3,4
),(�
5,8)
,(7,
8)}
(�3,
�1)
,(1,
1),(
1,2)
,(1,
3)}
BA
SEB
ALL
For
Exe
rcis
es 5
an
d 6
,use
th
e gr
aph
th
at
show
s th
e b
atti
ng
aver
age
for
Bar
ry B
ond
s of
th
e S
anF
ran
cisc
o G
ian
ts.
Sour
ce: w
ww.sp
ortsi
llustr
ated
.cnn.
com
5.F
ind
the
dom
ain
an
d es
tim
ate
the
ran
ge.
D �
{199
6,19
97,1
998,
1999
,200
0,20
01};
R �
{.26
2,.2
91,.
303,
.306
,.30
8,.3
28}
6.W
hic
h s
easo
ns
did
Bon
ds h
ave
the
low
est
and
hig
hes
t ba
ttin
g av
erag
es?
low
est:
1999
,hig
hes
t:20
01
MET
EOR
SF
or E
xerc
ises
7 a
nd
8,u
se t
he
ta
ble
th
at s
how
s th
e n
um
ber
of
met
eors
An
n o
bse
rved
eac
h h
our
du
rin
g a
met
eor
show
er.
7.W
hat
are
th
e do
mai
n a
nd
ran
ge?
D �
{12,
1,2,
3,4}
;R
�{1
5,26
,28}
8.G
raph
th
e re
lati
on.
Tim
e (A
.M.)
Mete
or
Sh
ow
er
Number of Meteors
12–1
1–2
2–3
3–4
4–5
0
30 25 20 15 10
Tim
eN
um
ber
of
(A.M
.)M
eteo
rs
1215
126
228
328
415
Year
Barr
y B
on
ds’
Batt
ing
Average
’96
’98
’97
’99
’00
’01
’02
0
.34
.32
.30
.28
.26
x
y
O
XY 5
�5 3 7
9�
6 4 8
xy
09
�8
3
2�
6
1 4
XY 3 4
�2 1
x
y
O
xy
43
�1
4
3�
2
23
�2
1
Pra
ctic
e (
Ave
rag
e)
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-3
4-3
Answers (Lesson 4-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csR
elat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-3
4-3
©G
lenc
oe/M
cGra
w-H
ill22
9G
lenc
oe A
lgeb
ra 1
Lesson 4-3
Pre-
Act
ivit
yH
ow c
an r
elat
ion
s b
e u
sed
to
rep
rese
nt
bas
ebal
l st
atis
tics
?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-3
at
the
top
of p
age
205
in y
our
text
book
.
In 1
997,
Ken
Gri
ffey
,Jr.
had
h
ome
run
s an
d st
rike
outs
.
Th
is c
an b
e re
pres
ente
d w
ith
th
e or
dere
d pa
ir (
,).
Rea
din
g t
he
Less
on
1.L
ook
at p
age
205
in y
our
text
book
.Th
ere
you
see
th
e sa
me
rela
tion
rep
rese
nte
d by
a s
etof
ord
ered
pai
rs,a
tab
le,a
gra
ph,a
nd
a m
appi
ng.
a.In
th
e li
st o
f or
dere
d pa
irs,
wh
ere
do y
ou s
ee t
he
nu
mbe
rs f
or t
he
dom
ain
? th
en
um
bers
for
th
e ra
nge
?b
efo
re t
he
com
mas
;af
ter
the
com
mas
b.
Wh
at p
arts
of
the
tabl
e sh
ow t
he
dom
ain
an
d th
e ra
nge
?T
he
colu
mn
of
nu
mb
ers
un
der
th
e le
tter
xsh
ow
s th
e d
om
ain
,an
d t
he
colu
mn
of
nu
mb
ers
un
der
th
e le
tter
ysh
ow
s th
e ra
ng
e.
c.H
ow d
o th
e ta
ble,
the
grap
h,a
nd
the
map
pin
g sh
ow t
hat
th
ere
are
thre
e or
dere
dpa
irs
in t
he
rela
tion
?T
he
tab
le h
as t
hre
e ro
ws
of
nu
mb
ers,
the
gra
ph
sho
ws
thre
e p
oin
ts m
arke
d w
ith
do
ts,a
nd
th
e m
app
ing
use
s th
ree
arro
ws.
2.W
hic
h t
ells
you
mor
e ab
out
a re
lati
on,a
lis
t of
th
e or
dere
d pa
irs
in t
he
rela
tion
or
the
dom
ain
an
d ra
nge
of
the
rela
tion
? E
xpla
in.
Sam
ple
an
swer
:A
list
of
the
ord
ered
pai
rs t
ells
yo
u m
ore
.Yo
u c
an u
se it
to
fin
d t
he
do
mai
n a
nd
th
e ra
ng
e,an
dyo
u k
no
w e
xact
ly h
ow
th
e n
um
ber
s ar
e p
aire
d.I
f yo
u o
nly
kn
ow
th
ed
om
ain
an
d t
he
ran
ge,
you
can
no
t b
e su
re h
ow
th
e n
um
ber
s ar
e p
aire
d.
3.D
escr
ibe
how
you
wou
ld f
ind
the
inve
rse
of t
he
rela
tion
{(1
,2),
(2,4
),(3
,6),
(4,8
)}.
Sw
itch
th
e co
ord
inat
es in
eac
h o
rder
ed p
air
to g
et
{(2,
1),(
4,2)
,(6,
3),(
8,4)
}.
Hel
pin
g Y
ou
Rem
emb
er
4.T
he
firs
t le
tter
s in
tw
o w
ords
an
d th
eir
orde
r in
th
e al
phab
et c
an s
omet
imes
hel
p yo
ure
mem
ber
thei
r m
ath
emat
ical
mea
nin
g.T
wo
key
term
s in
th
is l
esso
n a
re d
omai
nan
dra
nge
.Des
crib
e h
ow t
he
alph
abet
met
hod
cou
ld h
elp
you
rem
embe
r th
eir
mea
nin
g.S
amp
le a
nsw
er:
dco
mes
fir
st f
or
the
firs
t co
ord
inat
e,r
com
es s
eco
nd
fo
rth
e se
con
d c
oo
rdin
ate.
121
5612
156
©G
lenc
oe/M
cGra
w-H
ill23
0G
lenc
oe A
lgeb
ra 1
Inve
rse
Rel
atio
ns
On
eac
h g
rid
bel
ow,p
lot
the
poi
nts
in
Set
s A
an
d B
.Th
en c
onn
ect
the
poi
nts
in
Set
A w
ith
th
e co
rres
pon
din
g p
oin
ts i
n S
et B
.Th
en f
ind
th
ein
vers
es o
f S
et A
an
d S
et B
,plo
t th
e tw
o se
ts,a
nd
con
nec
t th
ose
poi
nts
.
Set
AS
et B
(�4,
0)(0
,1)
(�3,
0)(0
,2)
(�2,
0)(0
,3)
(�1,
0)(0
,4)
Set
AS
et B
(�3,
�3)
(�2,
1)(�
2,�
2)(�
1,2)
(�1,
�1)
(0,3
)(0
,0)
(1,4
)
Set
AS
et B
(�4,
1)(3
,2)
(�3,
2)(3
,2)
(�2,
3)(3
,2)
(�1,
4)(3
,2)
13.W
hat
is
the
grap
hic
al r
elat
ion
ship
bet
wee
n t
he
lin
e se
gmen
ts y
ou d
rew
con
nec
tin
g po
ints
in
Set
s A
an
d B
an
d th
e li
ne
segm
ents
con
nec
tin
g po
ints
in t
he
inve
rses
of
thos
e tw
o se
ts?
An
swer
s w
ill v
ary.
A p
oss
ible
an
swer
is t
hat
th
e g
rap
hs
are
refl
ecte
d a
cro
ss t
he
line
y�
xby
th
eir
inve
rses
.
x
y
O
x
y
O
x
y
OEn
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-3
4-3
Inve
rse
Set
AS
et B
1.(0
,�4)
(1,0
)
2.(0
,�3)
(2,0
)
3.(0
,�2)
(3,0
)
4.(0
,�1)
(4,0
)
Inve
rse
Set
AS
et B
5.(�
3,�
3)(1
,�2)
6.(�
2,�
2)(2
,�1)
7.(�
1,�
1)(3
,0)
8.(0
,0)
(4,1
)
Inve
rse
Set
AS
et B
9.(1
,�4)
(2,3
)
10.
(2,�
3)(2
,3)
11.
(3,�
2)(2
,3)
12.
(4,�
1)(2
,3)
Answers (Lesson 4-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Eq
uat
ion
s as
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-4
4-4
©G
lenc
oe/M
cGra
w-H
ill23
1G
lenc
oe A
lgeb
ra 1
Lesson 4-4
Solv
e Eq
uat
ion
sT
he
equ
atio
n y
�3x
�4
is a
n e
xam
ple
of a
n e
qu
atio
n i
n t
wo
vari
able
sbe
cau
se i
t co
nta
ins
two
vari
able
s,x
and
y.T
he
solu
tion
of a
n e
quat
ion
in
tw
ova
riab
les
is a
n o
rder
ed p
air
of r
epla
cem
ents
for
th
e va
riab
les
that
res
ult
s in
a t
rue
stat
emen
t w
hen
su
bsti
tute
d in
to t
he
equ
atio
n.
Fin
d t
he
solu
tion
set
for
y
��
2x�
1,gi
ven
th
e re
pla
cem
ent
set
{(�
2,3)
,(0,
�1)
,(1,
�2)
,(3,
1)}.
Mak
e a
tabl
e.S
ubs
titu
te t
he
xan
d y-
valu
es o
f ea
chor
dere
d pa
ir i
nto
th
e eq
uat
ion
.
xy
y�
�2x
�1
Tru
e o
r Fa
lse
�2
33
��
2(�
2) �
1Tr
ue3
�3
0�
1�
1 �
�2(
0) �
1Tr
ue�
1 �
�1
1�
2�
2 �
�2(
1) �
1F
alse
�2
��
3
31
1 �
�2(
3) �
1F
alse
1 �
�7
Th
e or
dere
d pa
irs
(�2,
3),a
nd
(0,�
1) r
esu
lt i
n t
rue
stat
emen
ts.T
he
solu
tion
set
is
{(�
2,3)
,(0,
�1)
}.
Sol
ve b
�2a
�1
ifth
e d
omai
n i
s {�
2,�
1,0,
2,4}
.
Mak
e a
tabl
e.T
he
valu
es o
f a
com
efr
om t
he
dom
ain
.Su
bsti
tute
eac
hva
lue
of a
into
th
e eq
uat
ion
to
dete
rmin
e th
e co
rres
pon
din
g va
lues
of b
in t
he
ran
ge.
a2a
�1
b(a
,b)
�2
2(�
2) �
1�
5(�
2, �
5)
�1
2(�
1) �
1�
3(�
1, �
3)
02(
0) �
1�
1(0
, �
1)
22(
2) �
13
(2,
3)
42(
4) �
17
(4,
7)
Th
e so
luti
on s
et i
s {(
�2,
�5)
,(�
1,�
3),(
0,�
1),(
2,3)
,(4,
7)}.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
solu
tion
set
of
each
eq
uat
ion
,giv
en t
he
rep
lace
men
t se
t.
1.y
�3x
�1;
{(0,
1), �
,2�, �
�1,
��,(
�1,
�2)
}{(
0,1)
, �,2
�,(�
1,�
2)}
2.3x
�2y
�6;
{(�
2,3)
,(0,
1),(
0,�
3),(
2,0)
}{(
0,�
3),(
2,0)
}
3.2x
�5
�y;
{(1,
3),(
2,1)
,(3,
2),(
4,3)
}{(
1,3)
,(2,
1)}
Sol
ve e
ach
eq
uat
ion
if
the
dom
ain
is
(�4,
�2,
0,2,
4}.
4.x
�y
�4
{(�
4,8)
,(�
2,6)
,(0,
4),(
2,2)
(4,
0)}
5.y
��
4x�
6{(
�4,
10),
(�2,
2),(
0,�
6),(
2,�
14),
(4,�
22)}
6.5a
�2b
�10
{(�
4,�
15),
(�2,
�10
),(0
,�5)
,(2,
0),(
4,5)
}
7.3x
�2y
�12
{(�
4,�
12),
(�2,
�9)
,(0,
�6)
,(2,
�3)
(4,
0)}
8.6x
�3y
�18
{(�
4,14
),(�
2,10
),(0
,6),
(2,2
),(4
,�2)
}
9.4x
�8
�2y
{(�
4,�
4),(
�2,
0),(
0,4)
,(2,
8),(
4,12
)}
10.x
�y
�8
{(�
4,�
12),
(�2,
�10
),(0
,�8)
,(2,
�6)
(4,
�4)
}
11.2
x�
y�
10{(
�4,
18),
(�2,
14),
(0,1
0),(
2,6)
,(4,
2)}1 � 3
2 � 31 � 3
©G
lenc
oe/M
cGra
w-H
ill23
2G
lenc
oe A
lgeb
ra 1
Gra
ph
So
luti
on
Set
sYo
u c
an g
raph
th
e or
dere
d pa
irs
in t
he
solu
tion
set
of
aneq
uat
ion
in
tw
o va
riab
les.
Th
e do
mai
n c
onta
ins
valu
es r
epre
sen
ted
by t
he
ind
epen
den
tva
riab
le.T
he
ran
ge c
onta
ins
the
corr
espo
ndi
ng
valu
es r
epre
sen
ted
by t
he
dep
end
ent
vari
able
,wh
ich
are
det
erm
ined
by
the
give
n e
quat
ion
.
Sol
ve 4
x�
2y�
12 i
f th
e d
omai
n i
s (�
1,0,
2,4}
.Gra
ph
th
e so
luti
on s
et.
Fir
st s
olve
th
e eq
uat
ion
for
yin
ter
ms
of x
.4x
�2y
�12
Orig
inal
equ
atio
n
4x�
2y�
4x�
12 �
4xS
ubtr
act
4xfr
om e
ach
side
.
2y�
12 �
4xS
impl
ify.
�D
ivid
e ea
ch s
ide
by 2
.
y�
6 �
2xS
impl
ify.
12 �
4x�
22y � 2S
tudy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Eq
uat
ion
s as
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-4
4-4
Exam
ple
Exam
ple
Su
bsti
tute
eac
h v
alu
e of
xfr
om t
he
dom
ain
to
dete
rmin
e th
e co
rres
pon
din
g va
lue
of y
in t
he
ran
ge.
x6
�2x
y(x
,y)
�1
6 �
2(�
1)8
(�1,
8)
06
�2(
0)6
(0,
6)
26
�2(
2)2
(2,
2)
46
�2(
4)�
2(4
, �
2)
Gra
ph t
he
solu
tion
set
.
x
y
O
Exer
cises
Exer
cises
Sol
ve e
ach
eq
uat
ion
for
th
e gi
ven
dom
ain
.Gra
ph
th
e so
luti
on s
et.
1.x
�2y
�4
for
x�
{�2,
0,2,
4}2.
y�
�2x
�3
for
x�
{�2,
�1,
0,1}
{(�
2,3)
,(0,
2),(
2,1)
,(4,
0)}
{(�
2,1)
,(�
1,�
1),(
0,�
3),(
1,�
5)}
3.x
�3y
�6
for
x�
{�3,
0,3,
6}4.
2x�
4y�
8 fo
r x
�{�
4,�
2,0,
2}
{(�
3,�
3),(
0,�
2),(
3,�
1),(
6,0)
}{(
�4,
�4)
,(�
2,�
3),(
0,�
2),(
2,�
1)}
x
y
Ox
y
O
x
y
O
x
y
O
Answers (Lesson 4-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
Eq
uat
ion
s as
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-4
4-4
©G
lenc
oe/M
cGra
w-H
ill23
3G
lenc
oe A
lgeb
ra 1
Lesson 4-4
Fin
d t
he
solu
tion
set
for
eac
h e
qu
atio
n,g
iven
th
e re
pla
cem
ent
set.
1.y
�3x
�1;
{(2,
5),(
�2,
7),(
0,�
1),(
1,1)
}{(
2,5)
,(0,
�1)
}
2.y
�2x
�4;
{(�
1,�
2),(
�3,
2),(
1,6)
,(�
2,8)
}{(
1,6)
}
3.y
�7
�2x
;{(3
,1),
(4,�
1),(
5,�
3),(
�1,
5)}
{(3,
1),(
4,�
1),(
5,�
3)}
4.�
3x�
y�
2;{(
�3,
7),(
�2,
�4)
,(�
1,�
1),(
3,11
)}{(
�2,
�4)
,(�
1,�
1),(
3,11
)}
Sol
ve e
ach
eq
uat
ion
if
the
dom
ain
is
{�2,
�1,
0,2,
5}.
5.y
�x
�4
{(�
2,2)
,(�
1,3)
,(0,
4),(
2,6)
,(5,
9)}
6.y
�3x
�2
{(�
2,�
8),(
�1,
�5)
,(0,
�2)
,(2,
4),(
5,13
)}
7.y
�2x
�1
{(�
2,�
3),(
�1,
�1)
,(0,
1),(
2,5)
,(5,
11)}
8.x
�y
�2
{(�
2,�
4),(
�1,
�3)
,(0,
�2)
,(2,
0),(
5,3)
}
9.x
�3
�y
{(�
2,5)
,(�
1,4)
,(0,
3),(
2,1)
,(5,
�2)
}
10.2
x�
y�
4{(
�2,
8),(
�1,
6),(
0,4)
,(2,
0),(
5,�
6)}
11.2
x�
y�
7{(
�2,
�11
),(�
1,�
9),(
0,�
7),(
2,�
3),(
5,3)
}
12.4
x�
2y�
6{(
�2,
7),(
�1,
5),(
0,3)
,(2,
�1)
,(5,
�7)
}
Sol
ve e
ach
eq
uat
ion
for
th
e gi
ven
dom
ain
.Gra
ph
th
e so
luti
on s
et.
13.y
�2x
�5
for
x�
{�5,
�4,
�2,
�1,
0}14
.y�
2x�
3 fo
r x
�{�
1,1,
2,3,
4}
15.2
x�
y�
1 fo
r x
�{�
2,�
1,0,
2,3}
16.2
x�
2y�
6 fo
r x
�{�
3,�
1,3,
4,6}
{(�
3,�
6),
(�1,
�4)
,(3,
0),
(4,1
),(6
,3)}
x
y
O
{(�
2,5)
,(�
1,3)
,(0
,1),
(2,�
3),
(3,�
5)}
x
y
O
{(�
1,�
5),
(1,�
1),(
2,1)
,(3
,3),
(4,5
)}
x
y
O
{(�
5,�
5),
(�4,
�3)
,(�
2,1)
,(�
1,3)
,(0
,5)}
x
y
O
©G
lenc
oe/M
cGra
w-H
ill23
4G
lenc
oe A
lgeb
ra 1
Fin
d t
he
solu
tion
set
for
eac
h e
qu
atio
n,g
iven
th
e re
pla
cem
ent
set.
1.y
�2
�5x
;{(3
,12)
,(�
3,�
17),
(2,�
8),(
�1,
7)}
{(2,
�8)
,(�
1,7)
}
2.3x
�2y
��
1;{(
�1,
1),(
�2,
�2.
5),(
�1,
�1.
5),(
0,0.
5)}
{(�
2,�
2.5)
,(0,
0.5)
}
Sol
ve e
ach
eq
uat
ion
if
the
dom
ain
is
{�2,
�1,
2,3,
5}.
3.y
�4
�2x
{(�
2,8)
,(�
1,6)
,(2,
0),(
3,�
2),(
5,�
6)}
4.x
�8
�y
{(�
2,10
),(�
1,9)
,(2,
6),(
3,5)
,(5,
3)}
5.4x
�2y
�10
{(�
2,9)
,(�
1,7)
,(2,
1),(
3,�
1),(
5,�
5)}
6.3x
�6y
�12
{(�
2,�
3),(
�1,
�2.
5),(
2,�
1),(
3,�
0.5)
,(5,
0.5)
}
7.2x
�4y
�16
{(�
2,5)
,(�
1,4.
5),(
2,3)
,(3,
2.5)
,(5,
1.5)
}
8.x
�y
�6
{(�
2,�
16),
(�1,
�14
),(2
,�8)
,(3,
�6)
,(5,
�2)
}
Sol
ve e
ach
eq
uat
ion
for
th
e gi
ven
dom
ain
.Gra
ph
th
e so
luti
on s
et.
9.2x
�4y
�8
for
x�
{�4,
�3,
�2,
2,5}
10.
x�
y�
1 fo
r x
�{�
4,�
3,�
2,0,
4}
EAR
TH S
CIE
NC
EF
or E
xerc
ises
11
and
12,
use
th
e fo
llow
ing
info
rmat
ion
.E
arth
mov
es a
t a
rate
of
30 k
ilom
eter
s pe
r se
con
d ar
oun
d th
e S
un
.Th
e eq
uat
ion
d�
30t
rela
tes
the
dist
ance
din
kilo
met
ers
Ear
th m
oves
to
tim
e t
in s
econ
ds.
11.F
ind
the
set
of o
rder
ed p
airs
wh
en
t�
{10,
20,3
0,45
,70}
.{(
10,3
00),
(20,
600)
,(3
0,90
0),(
45,1
350)
,(70
,210
0)}
12.G
raph
th
e se
t of
ord
ered
pai
rs.
GEO
MET
RYF
or E
xerc
ises
13–
15,u
se t
he
foll
owin
g in
form
atio
n.
Th
e eq
uat
ion
for
th
e ar
ea o
f a
tria
ngl
e is
A�
bh.S
upp
ose
the
area
of
tria
ngl
e D
EF
is
30 s
quar
e in
ches
.
13.S
olve
th
e eq
uat
ion
for
h.
h�
14.S
tate
the
ind
epen
dent
and
dep
ende
nt v
aria
bles
.b
is in
dep
end
ent;
his
dep
end
ent.
15.C
hoo
se 5
val
ues
for
ban
d fi
nd
the
corr
espo
ndi
ng
valu
es f
or h
.S
amp
le a
nsw
er:
{(5,
12),
(6,1
0),(
10,6
),(1
2,5)
,(15
,4)}
60 � b
1 � 2
Tim
e (s
)
Dis
tan
ce E
art
h T
ravels
Distance (km)
010
2030
4050
6070
80
2400
2100
1800
1500
1200 900
600
300
{(�
4,3)
, ��3,
2�1 2� �,
(�2,
2),(
0,1)
,(4
,�1)
}x
y
O
{(�
4,�
4),
(�3,
�3.
5),
(�2,
�3)
,(2
,�1)
,(5,
0.5)
}
x
y
O
1 � 2
1 � 2
Pra
ctic
e (
Ave
rag
e)
Eq
uat
ion
s as
Rel
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-4
4-4
Answers (Lesson 4-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csE
qu
atio
ns
as R
elat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-4
4-4
©G
lenc
oe/M
cGra
w-H
ill23
5G
lenc
oe A
lgeb
ra 1
Lesson 4-4
Pre-
Act
ivit
yW
hy
are
equ
atio
ns
of r
elat
ion
s im
por
tan
t in
tra
veli
ng?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-4
at
the
top
of p
age
212
in y
our
text
book
.
•In
th
e eq
uat
ion
p�
0.69
d,p
repr
esen
ts
and
d
repr
esen
ts
.
•H
ow m
any
vari
able
s ar
e in
th
e eq
uat
ion
p�
0.69
d?
two
Rea
din
g t
he
Less
on
1.S
upp
ose
you
mak
e th
e fo
llow
ing
tabl
e to
sol
ve a
n e
quat
ion
th
at u
ses
the
dom
ain
{�
3,�
2,�
1,0,
1}.
xx
�4
y(x
,y)
�3
�3
�4
�7
(�3,
�7)
�2
�2
�4
�6
(�2,
�6)
�1
�1
�4
�5
(�1,
�5)
00
�4
�4
(0,
�4)
11
�4
�3
(1,
�3)
a.W
hat
is
the
equ
atio
n?
y�
x�
4
b.
Wh
ich
col
um
n s
how
s th
e d
omai
n?
the
firs
t co
lum
n
c.W
hic
h c
olu
mn
sh
ows
the
ran
ge?
the
thir
d c
olu
mn
d.
Wh
ich
col
um
n s
how
s th
e so
luti
on s
et?
the
fou
rth
co
lum
n
2.T
he
solu
tion
set
of
the
equ
atio
n y
�2x
for
a gi
ven
dom
ain
is
{(�
2,�
4),(
0,0)
,(2,
4),(
7,14
)}.T
ell
wh
eth
er e
ach
sen
ten
ce i
s tr
ue
or f
alse
.If
fals
e,re
plac
e th
e u
nde
rlin
ed w
ord(
s) t
o m
ake
a tr
ue
sen
ten
ce.
a.T
he
dom
ain
con
tain
s th
e va
lues
rep
rese
nte
d by
th
e in
depe
nde
nt
vari
able
.tr
ue
b.
Th
e do
mai
n c
onta
ins
the
nu
mbe
rs �
4,0,
4,an
d 14
.fa
lse;
ran
ge
c.F
or e
ach
nu
mbe
r in
th
e do
mai
n,t
he
ran
ge c
onta
ins
a co
rres
pon
din
g n
um
ber
that
is
ava
lue
of t
he
depe
nde
nt
vari
able
.tr
ue
3.W
hat
is
mea
nt
by “
solv
ing
an e
quat
ion
for
yin
ter
ms
of x
”?is
ola
tin
g y
on
on
e si
de
of
the
equ
atio
n
Hel
pin
g Y
ou
Rem
emb
er
4.R
emem
ber,
wh
en y
ou s
olve
an
equ
atio
n f
or a
giv
en v
aria
ble,
that
var
iabl
e be
com
es t
he
dep
end
ent
vari
able
.Wri
te a
n e
quat
ion
an
d de
scri
be h
ow y
ou w
ould
ide
nti
fy t
he
depe
nde
nt
vari
able
.S
amp
le a
nsw
er:
y�
3xsh
ow
s th
at y
ou
hav
e so
lved
fo
ry,
so y
is t
he
dep
end
ent
vari
able
.
do
llars
po
un
ds
©G
lenc
oe/M
cGra
w-H
ill23
6G
lenc
oe A
lgeb
ra 1
Co
ord
inat
e G
eom
etry
an
d A
rea
How
wou
ld y
ou f
ind
the
area
of
a tr
ian
gle
wh
ose
vert
ices
hav
e
the
coor
din
ates
A(-
1,2)
,B(1
,4),
and
C(3
,0)?
Wh
en a
fig
ure
has
no
side
s pa
rall
el t
o ei
ther
axi
s,th
e h
eigh
t an
d ba
se a
re d
iffi
cult
to
fin
d.
On
e m
eth
od o
f fi
ndi
ng
the
area
is
to e
ncl
ose
the
figu
re i
n a
re
ctan
gle
and
subt
ract
th
e ar
ea o
f th
e su
rrou
ndi
ng
tria
ngl
es
from
th
e ar
ea o
f th
e re
ctan
gle.
Are
a of
rec
tan
gle
DE
FC
�4
�4
�16
squ
are
un
its
Are
a of
tri
angl
e I
�(2
)(4)
�4
Are
a of
tri
angl
e II
�
(2)(
4) �
4
Are
a of
tri
angl
e II
I �
(2)(
2) �
2
Tot
al �
10 s
quar
e u
nit
s
Are
a of
tri
angl
e A
BC
�16
�10
,or
6 sq
uar
e u
nit
s
Fin
d t
he
area
s of
th
e fi
gure
s w
ith
th
e fo
llow
ing
vert
ices
.
1.A
(-4,
-6),
B(0
,4),
2.A
(6,-
2),B
(8,-
10),
3.A
(0,2
),B
(2,7
),C
(4,2
)C
(12,
-6)
C(6
,10)
,D(9
,-2)
24 s
qu
are
un
its
20 s
qu
are
un
its
55 s
qu
are
un
its
A
Dx
y
O
B
C
2
2
x
y
OA
B
C
2
2x
y
O
A
B
C2
2
1 � 21 � 21 � 2x
y
O
BE
III
II
I
D
F C
A
x
y
O
B
C
A
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-4
4-4
Answers (Lesson 4-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Gra
ph
ing
Lin
ear
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-5
4-5
©G
lenc
oe/M
cGra
w-H
ill23
7G
lenc
oe A
lgeb
ra 1
Lesson 4-5
Iden
tify
Lin
ear
Equ
atio
ns
A l
inea
r eq
uat
ion
is a
n e
quat
ion
th
at c
an b
e w
ritt
en i
nth
e fo
rm A
x�
By
�C
.Th
is i
s ca
lled
th
e st
and
ard
for
mof
a l
inea
r eq
uat
ion
.
Sta
nd
ard
Fo
rm o
f a
Lin
ear
Eq
uat
ion
Ax
�B
y�
C,
whe
re A
�0,
Aan
d B
are
not
both
zer
o, a
nd A
, B
, an
d C
are
inte
gers
who
se G
CF
is 1
.
Det
erm
ine
wh
eth
er y
�6
�3x
is a
lin
ear
equ
atio
n.I
f so
,wri
te t
he
equ
atio
nin
sta
nd
ard
for
m.
Fir
st r
ewri
te t
he
equ
atio
n s
o bo
th v
aria
bles
are
on
the
sam
e si
de o
f th
e eq
uat
ion
.y
�6
�3x
Orig
inal
equ
atio
n
y�
3x�
6 �
3x�
3xA
dd 3
xto
eac
h si
de.
3x�
y�
6S
impl
ify.
Th
e eq
uat
ion
is
now
in
sta
nda
rd f
orm
,wit
h A
�3,
B�
1 an
d C
�6.
Th
is i
s a
lin
ear
equ
atio
n.
Det
erm
ine
wh
eth
er 3
xy�
y�
4 �
2xis
ali
nea
r eq
uat
ion
.If
so,w
rite
th
eeq
uat
ion
in
sta
nd
ard
for
m.
Sin
ce t
he
term
3xy
has
tw
o va
riab
les,
the
equ
atio
n c
ann
ot b
e w
ritt
en i
n t
he
form
Ax
�B
y�
C.T
her
efor
e,th
is i
sn
ot a
lin
ear
equ
atio
n.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Det
erm
ine
wh
eth
er e
ach
eq
uat
ion
is
a li
nea
r eq
uat
ion
.If
so,w
rite
th
e eq
uat
ion
in
stan
dar
d f
orm
.
1.2x
�4y
2.6
�y
�8
3.4x
�2y
��
1
yes;
2x�
4y�
0ye
s;y
�2
yes;
4x�
2y�
�1
4.3x
y�
8 �
4y5.
3x�
4 �
126.
y�
x2�
7
no
yes;
3x�
16n
o
7.y
�4x
�9
8.x
�8
�0
9.�
2x�
3 �
4y
yes;
4x�
y�
�9
yes;
x�
�8
yes;
2x�
4y�
3
10.2
�x
�y
11.
y�
12 �
4x12
.3xy
�y
�8
yes;
x�
2y�
�4
yes;
16x
�y
�48
no
13.6
x�
4y�
3 �
014
.yx
�2
�8
15.6
a�
2b�
8 �
b
yes;
6x�
4y�
3n
oye
s;6a
�3b
�8
16.
x�
12y
�1
17.3
�x
�x2
�0
18.x
2�
2xy
yes;
x�
48y
�4
no
no
1 � 4
1 � 41 � 2
©G
lenc
oe/M
cGra
w-H
ill23
8G
lenc
oe A
lgeb
ra 1
Gra
ph
Lin
ear
Equ
atio
ns
The
gra
ph o
f a
line
ar e
quat
ion
is a
line
.The
line
rep
rese
nts
all
solu
tion
s to
the
line
ar e
quat
ion.
Als
o,ev
ery
orde
red
pair
on
this
line
sat
isfi
es t
he e
quat
ion.
Gra
ph
th
e eq
uat
ion
y�
2x�
1.
Sol
ve t
he
equ
atio
n f
or y
.y
�2x
�1
Orig
inal
equ
atio
n
y�
2x�
2x�
1 �
2xA
dd 2
xto
eac
h si
de.
y�
2x�
1S
impl
ify.
Sel
ect
five
val
ues
for
th
e do
mai
n a
nd
mak
e a
tabl
e.T
hen
grap
h t
he
orde
red
pair
s an
d dr
aw a
lin
e th
rou
gh t
he
poin
ts.
x2x
�1
y(x
,y)
�2
2(�
2) �
1�
3(�
2, �
3)
�1
2(�
1) �
1�
1(�
1, �
1)
02(
0) �
11
(0,
1)
12(
1) �
13
(1,
3)
22(
2) �
15
(2,
5)
Gra
ph
eac
h e
qu
atio
n.
1.y
�4
2.y
�2x
3.x
�y
��
1
4.3x
�2y
�6
5.x
�2y
�4
6.2x
�y
��
2
7.3x
�6y
��
38.
�2x
�y
��
29.
x�
y�
6
x
y
O4
812
8 4x
y
Ox
y O
3 � 41 � 4
x
y Ox
y
Ox
y
O
x
y
Ox
y O
x
y
O
x
y O
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Gra
ph
ing
Lin
ear
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-5
4-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 4-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Gra
ph
ing
Lin
ear
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-5
4-5
©G
lenc
oe/M
cGra
w-H
ill23
9G
lenc
oe A
lgeb
ra 1
Lesson 4-5
Det
erm
ine
wh
eth
er e
ach
eq
uat
ion
is
a li
nea
r eq
uat
ion
.If
so,w
rite
th
e eq
uat
ion
in
stan
dar
d f
orm
.
1.xy
�6
2.y
�2
�3x
3.5x
�y
�4
no
yes;
3x�
y�
2ye
s;5x
�y
��
4
4.y
�2x
�5
5.y
��
7 �
6x6.
y�
3x2
�1
yes;
2x�
y�
�5
yes;
6x�
y�
7 n
o
7.y
�4
�0
8.5x
�6y
�3x
�2
9.y
�1
yes;
y�
4ye
s;x
�3y
�1
yes;
y�
2
Gra
ph
eac
h e
qu
atio
n.
10.y
�4
11.y
�3x
12.y
�x
�4
13.y
�x
�2
14.y
�4
�x
15.y
�4
�2x
16.x
�y
�3
17.1
0x�
�5y
18.4
x�
2y�
6
x
y
Ox
y
Ox
y
O
x
y
Ox
y
Ox
y
O
x
y
Ox
y
Ox
y
O
1 � 2
©G
lenc
oe/M
cGra
w-H
ill24
0G
lenc
oe A
lgeb
ra 1
Det
erm
ine
wh
eth
er e
ach
eq
uat
ion
is
a li
nea
r eq
uat
ion
.If
so,w
rite
th
e eq
uat
ion
in
stan
dar
d f
orm
.
1.4x
y�
2y�
92.
8x�
3y�
6 �
4x3.
7x�
y�
3 �
yn
oye
s;4x
�y
�2
yes;
7x�
�3
4.5
�2y
�3x
5.4y
�x
�9x
6.a
�b
�2
yes;
3x�
2y�
5ye
s;8x
�4y
�0
yes;
5a�
b�
10
7.6x
�2y
8.�
�1
9.�
�7
yes;
6x�
2y�
0ye
s;3x
�4y
�12
n
o
Gra
ph
eac
h e
qu
atio
n.
10.
x�
y�
211
.5x
�2y
�7
12.1
.5x
�3y
�9
CO
MM
UN
ICA
TIO
NS
For
Exe
rcis
es 1
3–15
,use
th
e fo
llow
ing
info
rmat
ion
.A
tel
eph
one
com
pan
y ch
arge
s $4
.95
per
mon
th f
or l
ong
dist
ance
cal
ls p
lus
$0.0
5 pe
r m
inu
te.T
he
mon
thly
cos
t c
of l
ong
dist
ance
cal
ls c
an b
e de
scri
bed
by t
he
equ
atio
n
c�
0.05
m�
4.95
,wh
ere
mis
th
e n
um
ber
of m
inu
tes.
13.F
ind
the
y-in
terc
ept
of t
he
grap
h o
f th
e eq
uat
ion
.(0
,4.9
5)
14.G
raph
th
e eq
uat
ion
.
15.I
f yo
u t
alk
140
min
ute
s,w
hat
is
the
mon
thly
cos
t fo
r lo
ng
dist
ance
?$1
1.95
MA
RIN
E B
IOLO
GY
For
Exe
rcis
es 1
6 an
d 1
7,u
se t
he
foll
owin
g in
form
atio
n.
Kil
ler
wh
ales
usu
ally
sw
im a
t a
rate
of
3.2–
9.7
kilo
met
ers
per
hou
r,th
ough
th
ey c
an t
rave
l u
p to
48.
4 ki
lom
eter
s pe
rh
our.
Su
ppos
e a
mig
rati
ng
kill
er w
hal
e is
sw
imm
ing
at a
nav
erag
e ra
te o
f 4.
5 ki
lom
eter
s pe
r h
our.
Th
e di
stan
ce d
the
wh
ale
has
tra
vele
d in
th
ours
can
be
pred
icte
d by
th
eeq
uat
ion
d�
4.5t
.
16.G
raph
th
e eq
uat
ion
.
17.U
se t
he
grap
h t
o pr
edic
t th
e ti
me
it t
akes
th
e ki
ller
w
hal
e to
tra
vel
30 k
ilom
eter
s.b
etw
een
6 h
an
d 7
hTi
me
(ho
urs
)
Kil
ler
Wh
ale
Tra
vels
Distance (km)
02
46
89
13
57
40 35 30 25 20 15 10 5
Tim
e (m
inu
tes)
Lon
g D
ista
nce
Cost ($)
040
8012
016
0
14 12 10 8 6 4 2
x
y
O
x
y
Ox
y
O
1 � 2
2 � y5 � x
y � 3x � 4
1 � 5
Pra
ctic
e (
Ave
rag
e)
Gra
ph
ing
Lin
ear
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-5
4-5
Answers (Lesson 4-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csG
rap
hin
g L
inea
r E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-5
4-5
©G
lenc
oe/M
cGra
w-H
ill24
1G
lenc
oe A
lgeb
ra 1
Lesson 4-5
Pre-
Act
ivit
yH
ow c
an l
inea
r eq
uat
ion
s b
e u
sed
in
nu
trit
ion
?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-5
at
the
top
of p
age
218
in y
our
text
book
.
In t
he
equ
atio
n f
�0.
3 ��,w
hat
are
th
e in
depe
nde
nt
and
depe
nde
nt
vari
able
s?C
is in
dep
end
ent,
fis
dep
end
ent.
Rea
din
g t
he
Less
on
1.D
escr
ibe
the
grap
h o
f a
lin
ear
equ
atio
n.
Th
e g
rap
h is
a s
trai
gh
t lin
e.
2.D
eter
min
e w
het
her
eac
h e
quat
ion
is
a li
nea
r eq
uat
ion
.Exp
lain
.
Eq
uat
ion
Lin
ear
or
no
n-l
inea
r?E
xpla
nat
ion
a.2x
�3y
�1
linea
rT
he
equ
atio
n c
an b
e w
ritt
en a
s 2x
�3y
�1.
b.
4xy
�2y
�7
no
n-l
inea
r4x
yh
as t
wo
var
iab
les.
c.2x
2�
4y�
3n
on
-lin
ear
Th
e va
riab
le x
has
an
exp
on
ent
of
2.
d.
��
2lin
ear
Th
e eq
uat
ion
can
be
wri
tten
as
3x�
20y
�30
.
3.W
hat
do
the
term
s x-
inte
rcep
tan
d y-
inte
rcep
tm
ean
?T
he
x-in
terc
ept
is t
he
x-co
ord
inat
e o
f th
e p
oin
t w
her
e th
e g
rap
h o
f an
eq
uat
ion
cro
sses
th
e x-
axis
,an
d t
he
y-in
terc
ept
is t
he
y-co
ord
inat
e o
f th
e p
oin
t w
her
e th
eg
rap
h c
ross
es t
he
y-ax
is.
Hel
pin
g Y
ou
Rem
emb
er
4.D
escr
ibe
the
met
hod
you
wou
ld u
se t
o gr
aph
4x
�2y
�8.
Sam
ple
an
swer
:F
ind
th
ex-
an
d y
-in
terc
epts
,wh
ich
are
2 a
nd
4.P
lot
the
po
ints
fo
r th
e o
rder
edp
airs
(2,
0) a
nd
(0,
4),a
nd
dra
w a
lin
e th
at c
on
nec
ts t
he
po
ints
.
4y � 3x � 5
C � 9
©G
lenc
oe/M
cGra
w-H
ill24
2G
lenc
oe A
lgeb
ra 1
Taxi
cab
Gra
ph
sYo
u h
ave
use
d a
rect
angu
lar
coor
din
ate
syst
em t
o gr
aph
eq
uat
ion
s su
ch a
s y
�x
�1
on a
coo
rdin
ate
plan
e.In
a
coor
din
ate
plan
e,th
e n
um
bers
in
an
ord
ered
pai
r (x
,y)
can
be
an
y tw
o re
al n
um
bers
.
A t
axic
ab p
lan
eis
dif
fere
nt
from
th
e u
sual
coo
rdin
ate
plan
e.T
he
only
poi
nts
all
owed
are
th
ose
that
exi
st a
lon
g th
e h
oriz
onta
l an
d ve
rtic
al g
rid
lin
es.Y
ou m
ay t
hin
k of
th
e po
ints
as
tax
icab
s th
at m
ust
sta
y on
th
e st
reet
s.
Th
e ta
xica
b gr
aph
sh
ows
the
equ
atio
ns
y�
�2
and
y�
x�
1.N
otic
e th
at o
ne
of t
he
grap
hs
is n
o lo
nge
r a
stra
igh
t li
ne.
It i
s n
ow a
col
lect
ion
of
sepa
rate
poi
nts
.
Gra
ph
th
ese
equ
atio
ns
on t
he
taxi
cab
pla
ne
at t
he
righ
t.
1.y
�x
�1
2.y
��
2x�
3
3.y
�2.
54.
x�
�4
Use
you
r gr
aph
s fo
r th
ese
pro
ble
ms.
5.W
hic
h o
f th
e eq
uat
ion
s h
as t
he
sam
e gr
aph
in
bot
h t
he
usu
al c
oord
inat
e pl
ane
and
the
taxi
cab
plan
e?x
��
4
6.D
escr
ibe
the
form
of
equ
atio
ns
that
hav
e th
e sa
me
grap
h i
n b
oth
th
e u
sual
coo
rdin
ate
plan
e an
d th
e ta
xica
b pl
ane.
x�
Aan
d y
�B
,wh
ere
Aan
d B
are
inte
ger
s
In t
he
taxi
cab
pla
ne,
dis
tan
ces
are
not
mea
sure
d d
iago
nal
ly,b
ut
alon
g th
e st
reet
s.W
rite
th
e ta
xi-d
ista
nce
bet
wee
n e
ach
pai
r of
poi
nts
.
7.(0
,0)
and
(5,2
)8.
(0,0
) an
d (-
3,2)
9.(0
,0)
and
(2,1
.5)
7 u
nit
s5
un
its
3.5
un
its
10.(
1,2)
an
d (4
,3)
11.(
2,4)
an
d (-
1,3)
12.(
0,4)
an
d (-
2,0)
4 u
nit
s4
un
its
6 u
nit
s
Dra
w t
hes
e gr
aph
s on
th
e ta
xica
b g
rid
at
the
righ
t.
13.T
he
set
of p
oin
ts w
hos
e ta
xi-d
ista
nce
fro
m (
0,0)
is
2 u
nit
s.in
dic
ated
by
cro
sses
14.T
he
set
of p
oin
ts w
hos
e ta
xi-d
ista
nce
fro
m (
2,1)
is
3 u
nit
s.in
dic
ated
by
do
ts
x
y
O
x
y
O
1.
1.2.
2.
3.3.
4. 4.
x
y
O
y �
x �
1
y �
�2
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-5
4-5
Answers (Lesson 4-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-6
4-6
©G
lenc
oe/M
cGra
w-H
ill24
3G
lenc
oe A
lgeb
ra 1
Lesson 4-6
Iden
tify
Fu
nct
ion
sR
elat
ion
s in
wh
ich
eac
h e
lem
ent
of t
he
dom
ain
is
pair
ed w
ith
exac
tly
one
elem
ent
of t
he
ran
ge a
re c
alle
d fu
nct
ion
s.
Det
erm
ine
wh
eth
er t
he
rela
tion
{(6
,�3)
,(4
,1),
(7,�
2),(
�3,
1)}
is a
fun
ctio
n.E
xpla
in.
Sin
ce e
ach
ele
men
t of
th
e do
mai
n i
spa
ired
wit
h e
xact
ly o
ne
elem
ent
ofth
e ra
nge
,th
is r
elat
ion
is
afu
nct
ion
.
Det
erm
ine
wh
eth
er 3
x�
y�
6 is
a f
un
ctio
n.
Sin
ce t
he
equ
atio
n i
s in
th
e fo
rm
Ax
�B
y�
C,t
he
grap
h o
f th
eeq
uat
ion
wil
l be
a l
ine,
as s
how
nat
th
e ri
ght.
If y
ou d
raw
a v
erti
cal
lin
e th
rou
gh e
ach
val
ue
of x
,th
eve
rtic
al l
ine
pass
es t
hro
ugh
just
one
poin
t of
th
e gr
aph
.Th
us,
the
lin
e re
pres
ents
a f
un
ctio
n.
x
y
O
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n.
1.2.
3.
yes
yes
no
4.5.
6.
no
no
yes
7.{(
4,2)
,(2,
3),(
6,1)
}8.
{(�
3,�
3),(
�3,
4),(
�2,
4)}
9.{(
�1,
0),(
1,0)
}ye
sn
oye
s
10.�
2x�
4y�
011
.x2
�y2
�8
12.x
��
4ye
sn
on
o
x
y
Ox
y
Ox
y O
XY
�1 0 1 2
4 5 6 7
x
y
Ox
y
O
©G
lenc
oe/M
cGra
w-H
ill24
4G
lenc
oe A
lgeb
ra 1
Fun
ctio
n V
alu
esE
quat
ion
s th
at a
re f
un
ctio
ns
can
be
wri
tten
in
a f
orm
cal
led
fun
ctio
nn
otat
ion
.For
exa
mpl
e,y
�2x
�1
can
be
wri
tten
as
f(x)
�2x
�1.
In t
he
fun
ctio
n,x
repr
esen
ts t
he
elem
ents
of
the
dom
ain
,an
d f(
x) r
epre
sen
ts t
he
elem
ents
of
the
ran
ge.
Su
ppos
e yo
u w
ant
to f
ind
the
valu
e in
th
e ra
nge
th
at c
orre
spon
ds t
o th
e el
emen
t 2
in t
he
dom
ain
.Th
is i
s w
ritt
en f
(2)
and
is r
ead
“fof
2.”
Th
e va
lue
of f
(2)
is f
oun
d by
su
bsti
tuti
ng
2 fo
r x
in t
he
equ
atio
n.
If f
(x)
�3x
�4,
fin
d e
ach
val
ue.
a.f(
3)f(
3) �
3(3)
�4
Rep
lace
xw
ith 3
.
�9
�4
Mul
tiply
.
�5
Sim
plify
.
b.
f(�
2)f(
�2)
�3(
�2)
�4
Rep
lace
xw
ith �
2.
��
6 �
4M
ultip
ly.
��
10S
impl
ify.
If f
(x)
�2x
�4
and
g(x
) �
x2�
4x,f
ind
eac
h v
alu
e.
1.f(
4)2.
g(2)
3.f(
�5)
4�
4�
14
4.g(
�3)
5.f(
0)6.
g(0)
21�
40
7.f(
3) �
18.
f ��
9.g �
�1
�3
�
10.f
(a2 )
11.f
(k�
1)12
.g(2
c)
2a2
�4
2k�
24c
2�
8c
13.f
(3x)
14.f
(2)
�3
15.g
(�4)
6x�
43
32
15 � 161 � 2
1 � 41 � 4
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-6
4-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 4-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-6
4-6
©G
lenc
oe/M
cGra
w-H
ill24
5G
lenc
oe A
lgeb
ra 1
Lesson 4-6
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n.
1.ye
s2.
yes
3.n
o
4.ye
s5.
no
6.n
o
7.{(
2,5)
,(4,
�2)
,(3,
3),(
5,4)
,(�
2,5)
}ye
s8.
{(6,
�1)
,(�
4,2)
,(5,
2),(
4,6)
,(6,
5)}
no
9.y
�2x
�5
yes
10.y
�11
yes
11.
yes
12.
no
13.
no
If f
(x)
�3x
�2
and
g(x
) �
x2�
x,fi
nd
eac
h v
alu
e.
14.f
(4)
1415
.f(8
)26
16.f
(�2)
�4
17.g
(2)
2
18.g
(�3)
1219
.g(�
6)42
20.f
(2)
�1
921
.f(1
) �
14
22.g
(2)
�2
023
.g(�
1) �
46
24.f
(x�
1)3x
�5
25.g
(3b)
9b2
�3b
x
y
Ox
y
Ox
y
O
xy
37
�1
1
10
35
73
xy
27
5�
3
35
�4
�2
52
xy
4�
5
�1
�10
0�
9
1�
7
91
XY 2�
1 3 5
4 6 7
XY 4 1�
2
5 2 0�
3
XY 4 1
�3
�5
�6
�2 1 3
©G
lenc
oe/M
cGra
w-H
ill24
6G
lenc
oe A
lgeb
ra 1
Det
erm
ine
wh
eth
er e
ach
rel
atio
n i
s a
fun
ctio
n.
1.ye
s2.
no
3.ye
s
4.{(
1,4)
,(2,
�2)
,(3,
�6)
,(�
6,3)
,(�
3,6)
}5.
{(6,
�4)
,(2,
�4)
,(�
4,2)
,(4,
6),(
2,6)
}ye
sn
o
6.x
��
2 n
o7.
y�
2 ye
s
If f
(x)
�2x
�6
and
g(x
) �
x�
2x2 ,
fin
d e
ach
val
ue.
8.f(
2)�
29.
f ����
710
.g(�
1)�
3
11.g
����
12.f
(7)
�9
�1
13.g
(�3)
�13
�8
14.f
(h�
9)15
.g(3
y)16
.2[g
(b)
�1]
2h�
123y
�18
y22b
�4b
2�
2
WA
GE
SF
or E
xerc
ises
17
and
18,
use
th
e fo
llow
ing
info
rmat
ion
.
Mar
tin
ear
ns
$7.5
0 pe
r h
our
proo
frea
din
g ad
s at
a l
ocal
new
spap
er.H
is w
eekl
y w
age
wca
nbe
des
crib
ed b
y th
e eq
uat
ion
w�
7.5h
,wh
ere
his
th
e n
um
ber
of h
ours
wor
ked.
17.W
rite
th
e eq
uat
ion
in
fu
nct
ion
al n
otat
ion
.f(
h)
�7.
5h
18.F
ind
f(15
),f(
20),
and
f(25
).11
2.50
,150
,187
.50
ELEC
TRIC
ITY
For
Exe
rcis
es 1
9–21
,use
th
e fo
llow
ing
info
rmat
ion
.
Th
e ta
ble
show
s th
e re
lati
onsh
ip b
etw
een
res
ista
nce
Ran
d cu
rren
t I
in a
cir
cuit
.
19.I
s th
e re
lati
onsh
ip a
fu
nct
ion
?E
xpla
in.Y
es;
for
each
val
ue
in t
he
do
mai
n,t
her
eis
on
ly o
ne
valu
e in
th
e ra
ng
e.
20.I
f th
e re
lati
on c
an b
e re
pres
ente
d by
th
e eq
uat
ion
IR
�12
,rew
rite
th
e eq
uat
ion
in
fu
nct
ion
al n
otat
ion
so
that
th
e re
sist
ance
Ris
a f
un
ctio
n o
f th
e cu
rren
t I.
f(I)
�
21.W
hat
is
the
resi
stan
ce i
n a
cir
cuit
wh
en t
he
curr
ent
is 0
.5 a
mpe
re?
24 o
hm
s
12 � I
Res
ista
nce
(o
hm
s)12
080
486
4
Cu
rren
t (a
mp
eres
)0.
10.
150.
252
3
5 � 91 � 3
1 � 2
x
y
O
xy
1�
5
�4
3
76
1�
2
XY 0 3�
2
�3
�2 1 5
Pra
ctic
e (
Ave
rag
e)
Fu
nct
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-6
4-6
Answers (Lesson 4-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csF
un
ctio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-6
4-6
©G
lenc
oe/M
cGra
w-H
ill24
7G
lenc
oe A
lgeb
ra 1
Lesson 4-6
Pre-
Act
ivit
yH
ow a
re f
un
ctio
ns
use
d i
n m
eteo
rolo
gy?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-6
at
the
top
of p
age
226
in y
our
text
book
.
If p
ress
ure
is
the
inde
pen
den
t va
riab
le a
nd
tem
pera
ture
is
the
depe
nde
nt
vari
able
,wh
at a
re t
he
orde
red
pair
s fo
r th
is s
et o
f da
ta?
{(10
13,3
),(1
006,
4),(
997,
10),
(995
,13)
,(99
5,8)
,(10
00,4
),(1
006,
1),(
1011
,�2)
,(10
16,�
6),(
1019
,�9)
}
Rea
din
g t
he
Less
on
1.T
he
stat
emen
t,“R
elat
ion
s in
wh
ich
eac
h e
lem
ent
of t
he
is p
aire
d w
ith
exa
ctly
on
e el
emen
t of
th
e ar
e ca
lled
fu
nct
ion
s,”
is f
alse
.How
can
you
ch
ange
th
e u
nde
rlin
ed
wor
ds t
o m
ake
the
stat
emen
t tr
ue?
Ch
ang
e ra
ng
eto
do
mai
nan
d d
om
ain
to r
ang
e.
2.D
escr
ibe
how
eac
h m
eth
od s
how
s th
at t
he
rela
tion
rep
rese
nte
d is
a f
un
ctio
n.
a.m
appi
ng
Th
e el
emen
ts o
f th
e d
om
ain
are
pai
red
wit
h c
orr
esp
on
din
gel
emen
ts in
th
e ra
ng
e.E
ach
elem
ent
of
the
do
mai
n h
as o
nly
on
e ar
row
go
ing
fro
m it
.
b.
vert
ical
lin
e te
stN
o v
erti
cal l
ine
pas
ses
thro
ug
hm
ore
th
an o
ne
po
int
of
the
gra
ph
.
Hel
pin
g Y
ou
Rem
emb
er
3.A
stu
den
t w
ho
was
try
ing
to h
elp
a fr
ien
d re
mem
ber
how
fu
nct
ion
s ar
e di
ffer
ent
from
rela
tion
s th
at a
re n
ot f
un
ctio
ns
gave
th
e fo
llow
ing
advi
ce:J
ust
rem
embe
r th
at f
un
ctio
ns
are
very
str
ict
and
nev
er g
ive
you
a c
hoi
ce.E
xpla
in h
ow t
his
mig
ht
hel
p yo
u r
emem
ber
wh
at a
fu
nct
ion
is.
Sam
ple
an
swer
:A
fu
nct
ion
alw
ays
pai
rs e
ach
ele
men
t in
the
do
mai
n w
ith
exa
ctly
on
e el
emen
t in
th
e ra
ng
e.If
tw
o p
eop
le s
tart
wit
hth
e sa
me
elem
ent
of
the
do
mai
n,t
hey
are
fo
rced
to
pai
r it
wit
h t
he
sam
eel
emen
t in
th
e ra
ng
e.T
he
seco
nd
per
son
can
no
t p
ick
a d
iffe
ren
t n
um
ber
fro
m t
he
firs
t p
erso
n.
x
y
O
XY 1 2 3 7
�2
�1 0 4
dom
ain
ran
ge
©G
lenc
oe/M
cGra
w-H
ill24
8G
lenc
oe A
lgeb
ra 1
Co
mp
osi
te F
un
ctio
ns
Th
ree
thin
gs a
re n
eede
d to
hav
e a
fun
ctio
n—
a se
t ca
lled
th
e do
mai
n,
a se
t ca
lled
th
e ra
nge
,an
d a
rule
th
at m
atch
es e
ach
ele
men
t in
th
edo
mai
n w
ith
on
ly o
ne
elem
ent
in t
he
ran
ge.H
ere
is a
n e
xam
ple.
Ru
le:f
(x)
�2x
�1
f(x)
�2x
�1
f(1)
�2(
1) �
1 �
2 �
1 �
3
f(2)
�2(
2) �
1 �
4 �
1 �
5
f(-3
) �
2(�
3) �
1 �
�6
�1
��
5
Su
ppos
e w
e h
ave
thre
e se
ts A
,B,a
nd
C a
nd
two
fun
ctio
ns
desc
ribe
das
sh
own
bel
ow.
Ru
le:f
(x)
�2x
�1
Ru
le:g
(y)
�3y
�4
g(y)
�3y
�4
g(3)
�3(
3) �
4 �
5
Let
’s f
ind
a ru
le t
hat
wil
l m
atch
ele
men
ts o
f se
t A
wit
h e
lem
ents
of
set
C w
ith
out
fin
din
g an
y el
emen
ts i
n s
et B
.In
oth
er w
ords
,let
’s f
ind
a ru
le f
or t
he
com
pos
ite
fun
ctio
n g
[f(x
)].
Sin
ce f
(x)
�2x
�1,
g[f(
x)]
�g(
2x�
1).
Sin
ce g
(y)
�3y
�4,
g(2x
�1)
�3(
2x�
1) �
4,or
6x
�1.
Th
eref
ore,
g[f(
x)]
�6x
�1.
Fin
d a
ru
le f
or t
he
com
pos
ite
fun
ctio
n g
[f(x
)].
1.f(
x) �
3xan
d g(
y) �
2y�
12.
f(x)
�x2
�1
and
g(y)
�4y
g[f
(x)]
�6x
�1
g[f
(x)]
�4x
2�
4
3.f(
x) �
�2x
and
g(y)
�y2
�3y
4.f(
x) �
and
g(y)
�y�
1
g[f
(x)]
�4x
2�
6xg
[f(x
)] �
x�
3
5.Is
it
alw
ays
the
case
th
at g
[f(x
)] �
f[g(
x)]?
Ju
stif
y yo
ur
answ
er.
No
.Fo
r ex
amp
le,i
n E
xerc
ise
1,f[
g(x
)] �
f(2x
�1)
�3(
2x�
1) �
6x�
3,n
ot
6x�
1.
1� x
�3
13
xf (
x)
5
g[f(
x)]
AB
C
13
25
–3–5
xf(
x)
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-6
4-6
Answers (Lesson 4-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Ari
thm
etic
Seq
uen
ces
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-7
4-7
©G
lenc
oe/M
cGra
w-H
ill24
9G
lenc
oe A
lgeb
ra 1
Lesson 4-7
Rec
og
niz
e A
rith
met
ic S
equ
ence
sA
seq
uen
ceis
a s
et o
f n
um
bers
in
a s
peci
fic
orde
r.If
th
e di
ffer
ence
bet
wee
n s
ucc
essi
ve t
erm
s is
con
stan
t,th
en t
he
sequ
ence
is
call
ed a
nar
ith
met
ic s
equ
ence
.
Ari
thm
etic
Seq
uen
cea
num
eric
al p
atte
rn t
hat
incr
ease
s or
dec
reas
es a
t a
cons
tant
rat
e or
val
ue c
alle
d th
eco
mm
on
dif
fere
nce
Det
erm
ine
wh
eth
er t
he
seq
uen
ce 1
,3,5
,7,9
,11,
… i
s an
arit
hm
etic
seq
uen
ce.J
ust
ify
you
ran
swer
.
If p
ossi
ble,
fin
d th
e co
mm
on d
iffe
ren
cebe
twee
n t
he
term
s.S
ince
3 �
1 �
2,5
�3
�2,
and
so o
n,t
he
com
mon
dif
fere
nce
is 2
.
Sin
ce t
he
diff
eren
ce b
etw
een
th
e te
rms
of
1,3,
5,7,
9,11
,… i
s co
nst
ant,
this
is
anar
ith
met
ic s
equ
ence
.
Det
erm
ine
wh
eth
er t
he
seq
uen
ce 1
,2,4
,8,1
6,32
,… i
s an
arit
hm
etic
seq
uen
ce.J
ust
ify
you
ran
swer
.
If p
ossi
ble,
fin
d th
e co
mm
on d
iffe
ren
cebe
twee
n t
he
term
s.S
ince
2 �
1 �
1 an
d 4
�2
�2,
ther
e is
no
com
mon
dif
fere
nce
.
Sin
ce t
he
diff
eren
ce b
etw
een
th
e te
rms
of
1,2,
4,8,
16,3
2,…
is
not
con
stan
t,th
is i
sn
ot a
n a
rith
met
ic s
equ
ence
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Det
erm
ine
wh
eth
er e
ach
seq
uen
ce i
s an
ari
thm
etic
seq
uen
ce.I
f it
is,
stat
e th
eco
mm
on d
iffe
ren
ce.
1.1,
5,9,
13,1
7,…
2.8,
4,0,
�4,
�8,
…3.
1,3,
9,27
,81,
…
yes;
4ye
s;�
4n
o
4.10
,15,
25,4
0,60
,…5.
�10
,�5,
0,5,
10,…
6.8,
6,4,
2,0,
�2,
…
no
yes;
5ye
s;�
2
7.4,
8,12
,16,
…8.
15,1
2,10
,9,…
9.1.
1,2.
1,3.
1,4.
1,5.
1,…
yes;
4n
oye
s;1
10.8
,7,6
,5,4
,…11
.0.5
,1.5
,2.5
,3.5
,4.5
,…12
.1,4
,16,
64,…
yes;
�1
yes;
1n
o
13.1
0,14
,18,
22,…
14.�
3,�
6,�
9,�
12,…
15.7
,0,�
7,�
14,…
yes;
4ye
s;�
3ye
s;�
7
©G
lenc
oe/M
cGra
w-H
ill25
0G
lenc
oe A
lgeb
ra 1
Wri
te A
rith
met
ic S
equ
ence
sYo
u c
an u
se t
he
com
mon
dif
fere
nce
of
an a
rith
met
icse
quen
ce t
o fi
nd
the
nex
t te
rm o
f th
e se
quen
ce.E
ach
ter
m a
fter
th
e fi
rst
term
is
fou
nd
byad
din
g th
e pr
eced
ing
term
an
d th
e co
mm
on d
iffe
ren
ce.
Term
s o
f an
Ari
thm
etic
Seq
uen
ceIf
a 1is
the
firs
t te
rm o
f an
arit
hmet
ic s
eque
nce
with
com
mon
di
ffere
nce
d, t
hen
the
sequ
ence
is a
1, a
1�
d, a
1�
2d,
a 1�
3d,
….
nth
Ter
m o
f an
Ari
thm
etic
Seq
uen
cea n
�a 1
�(n
�1)
d
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Ari
thm
etic
Seq
uen
ces
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-7
4-7
Fin
d t
he
nex
t th
ree
term
s of
th
e ar
ith
met
ic s
equ
ence
28,
32,3
6,40
,….
Fin
d th
e co
mm
on d
iffe
ren
ce b
ysu
btra
ctin
g su
cces
sive
ter
ms.
Th
e co
mm
on d
iffe
ren
ce i
s 4.
Add
4 t
o th
e la
st g
iven
ter
m,4
0,to
get
the
nex
t te
rm.C
onti
nu
e ad
din
g 4
un
til
the
nex
t th
ree
term
s ar
e fo
un
d.
Th
e n
ext
thre
e te
rms
are
44,4
8,52
.
40
� 4
� 4
� 4
4448
52
28
� 4
� 4
� 4
3236
40
Wri
te a
n e
qu
atio
n f
or t
he
nth
ter
m o
f th
e se
qu
ence
12,
15,1
8,21
,… .
In t
his
seq
uen
ce,a
1is
12.
Fin
d th
e co
mm
ondi
ffer
ence
.
Th
e co
mm
on d
iffe
ren
ce i
s 3.
Use
th
e fo
rmu
la f
or t
he
nth
ter
m t
o w
rite
an
equ
atio
n.
a n�
a 1�
(n�
1)d
For
mul
a fo
r th
e nt
h te
rm
a n�
12 �
(n�
1)3
a 1�
12,
d�
3
a n�
12 �
3n�
3D
istr
ibut
ive
Pro
pert
y
a n�
3n�
9S
impl
ify.
Th
e eq
uat
ion
for
th
e n
th t
erm
is
a n�
3n�
9.
12
� 3
� 3
� 3
1518
21
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
nex
t th
ree
term
s of
eac
h a
rith
met
ic s
equ
ence
.
1.9,
13,1
7,21
,25,
…2.
4,0,
�4,
�8,
�12
,…3.
29,3
5,41
,47,
…29
,33,
37�
16,�
20,�
2453
,59,
654.
�10
,�5,
0,5,
…5.
2.5,
5,7.
5,10
,…6.
3.1,
4.1,
5.1,
6.1,
…10
,15,
2012
.5,1
5,17
.57.
1,8.
1,9.
1
Fin
d t
he
nth
ter
m o
f ea
ch a
rith
met
ic s
equ
ence
des
crib
ed.
7.a 1
�6,
d�
3,n
�10
8.a 1
��
2,d
��
3,n
�8
9.a 1
�1,
d�
�5,
n�
2033
�23
�94
10.a
1�
�3,
d�
�2,
n�
5011
.a1
��
12,d
�4,
n�
2012
.a1
�1,
d�
,n�
11�
101
646
Wri
te a
n e
qu
atio
n f
or t
he
nth
ter
m o
f th
e ar
ith
met
ic s
equ
ence
.
13.1
,3,5
,7,…
14.�
1,�
4,�
7,�
10,…
15.�
4,�
9,�
14,�
19,…
a n�
2n�
1a n
��
3n�
2a n
��
5n�
1
1 � 2
Answers (Lesson 4-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Ari
thm
etic
Seq
uen
ces
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-7
4-7
©G
lenc
oe/M
cGra
w-H
ill25
1G
lenc
oe A
lgeb
ra 1
Lesson 4-7
Det
erm
ine
wh
eth
er e
ach
seq
uen
ce i
s an
ari
thm
etic
seq
uen
ce.I
f it
is,
stat
e th
eco
mm
on d
iffe
ren
ce.
1.4,
7,9,
12,…
no
2.15
,13,
11,9
,…ye
s;�
2
3.7,
10,1
3,16
,…ye
s;3
4.�
6,�
5,�
3,�
1,…
no
5.�
5,�
3,�
1,1,
…ye
s;2
6.�
9,�
12,�
15,�
18,…
yes;
�3
Fin
d t
he
nex
t th
ree
term
s of
eac
h a
rith
met
ic s
equ
ence
.
7.3,
7,11
,15,
…19
,23,
278.
22,2
0,18
,16,
…14
,12,
10
9.�
13,�
11,�
9,�
7,…
�5,
�3,
�1
10.�
2,�
5,�
8,�
11,…
�14
,�17
,�20
11.1
9,24
,29,
34,…
39,4
4,49
12.1
6,7,
�2,
�11
,…�
20,�
29,�
38
Fin
d t
he
nth
ter
m o
f ea
ch a
rith
met
ic s
equ
ence
des
crib
ed.
13.a
1�
6,d
�3,
n�
1239
14.a
1�
�2,
d�
5,n
�11
48
15.a
1�
10,d
��
3,n
�15
�32
16.a
1�
�3,
d�
�3,
n�
22�
66
17.a
1�
24,d
�8,
n�
2521
618
.a1
�8,
d�
�6,
n�
14�
70
19.8
,13,
18,2
3,…
for
n�
1788
20.�
10,�
3,4,
11,…
for
n�
1267
21.1
2,10
,8,6
,… f
or n
�16
�18
22.1
2,7,
2,�
3,…
for
n�
25�
108
Wri
te a
n e
qu
atio
n f
or t
he
nth
ter
m o
f ea
ch a
rith
met
ic s
equ
ence
.Th
en g
rap
h t
he
firs
t fi
ve t
erm
s of
th
e se
qu
ence
.
23.7
,13,
19,2
5,…
24.3
0,26
,22,
18,…
25.�
7,�
4,�
1,2,
…a n
�6n
�1
a n�
�4n
�34
a n�
3n�
10
n
a n
24
6
4
�4
�8O
n
a n
O2
46
30 20 10
n
a n
O2
46
30 20 10
©G
lenc
oe/M
cGra
w-H
ill25
2G
lenc
oe A
lgeb
ra 1
Det
erm
ine
wh
eth
er e
ach
seq
uen
ce i
s an
ari
thm
etic
seq
uen
ce.I
f it
is,
stat
e th
eco
mm
on d
iffe
ren
ce.
1.21
,13,
5,�
3,…
2.�
5,12
,29,
46,…
3.�
2.2,
�1.
1,0.
1,1.
3,…
yes;
�8
yes;
17n
o
Fin
d t
he
nex
t th
ree
term
s of
eac
h a
rith
met
ic s
equ
ence
.
4.82
,76,
70,6
4,…
5.�
49,�
35,�
21,�
7,…
6.,
,,0
,…
58,5
2,46
7,21
,35
�,�
,�
Fin
d t
he
nth
ter
m o
f ea
ch a
rith
met
ic s
equ
ence
des
crib
ed.
7.a 1
�7,
d�
9,n
�18
160
8.a 1
��
12,d
�4,
n�
3612
8
9.�
18,�
13,�
8,�
3,…
for
n�
2711
210
.4.1
,4.8
,5.5
,6.2
,… f
or n
�14
13.2
11.a
1�
,d�
,n�
153
12.a
1�
2,d
�1
,n�
2437
Wri
te a
n e
qu
atio
n f
or t
he
nth
ter
m o
f ea
ch a
rith
met
ic s
equ
ence
.Th
en g
rap
h t
he
firs
t fi
ve t
erm
s of
th
e se
qu
ence
.
13.9
,13,
17,2
1,…
14.�
5,�
2,1,
4,…
15.1
9,31
,43,
55,…
a n�
4n�
5a n
�3n
�8
a n�
12n
�7
BA
NK
ING
For
Exe
rcis
es 1
6 an
d 1
7,u
se t
he
foll
owin
g in
form
atio
n.
Ch
em d
epos
ited
$11
5.00
in
a s
avin
gs a
ccou
nt.
Eac
h w
eek
ther
eaft
er,h
e de
posi
ts $
35.0
0 in
toth
e ac
cou
nt.
16.W
rite
a f
orm
ula
to
fin
d th
e to
tal
amou
nt
Ch
em h
as d
epos
ited
for
an
y pa
rtic
ula
r n
um
ber
of w
eeks
aft
er h
is i
nit
ial
depo
sit.
a n�
35n
�11
5
17.H
ow m
uch
has
Ch
em d
epos
ited
30
wee
ks a
fter
his
in
itia
l de
posi
t?$1
165
18.S
TOR
E D
ISPL
AY
Tam
ika
is s
tack
ing
boxe
s of
tis
sue
for
a st
ore
disp
lay.
Eac
h r
ow o
fti
ssu
es h
as 2
few
er b
oxes
th
an t
he
row
bel
ow.T
he
firs
t ro
w h
as 2
3 bo
xes
of t
issu
es.H
owm
any
boxe
s w
ill
ther
e be
in
th
e te
nth
row
?5
n
a n
O2
46
60 40 20n
a n
24
6
8 4
�4O
n
a n
O2
46
30 20 10
1 � 21 � 2
7 � 81 � 4
3 � 8
3 � 41 � 2
1 � 4
1 � 41 � 2
3 � 4
Pra
ctic
e (
Ave
rag
e)
Ari
thm
etic
Seq
uen
ces
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-7
4-7
Answers (Lesson 4-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csA
rith
met
ic S
equ
ence
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-7
4-7
©G
lenc
oe/M
cGra
w-H
ill25
3G
lenc
oe A
lgeb
ra 1
Lesson 4-7
Pre-
Act
ivit
yH
ow a
re a
rith
met
ic s
equ
ence
s u
sed
to
solv
e p
rob
lem
s in
sci
ence
?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-7
at
the
top
of p
age
233
in y
our
text
book
.
Des
crib
e th
e pa
tter
n i
n t
he
data
.T
he
alti
tud
e o
f th
e p
rob
ein
crea
ses
by 8
.2 f
eet
each
sec
on
d.
Rea
din
g t
he
Less
on
1.D
o th
e re
cord
ed a
ltit
ude
s in
th
e in
trod
uct
ion
for
m a
n a
rith
met
ic s
equ
ence
? E
xpla
in.
Yes;
the
dif
fere
nce
bet
wee
n t
he
succ
essi
ve t
erm
s is
th
e co
nst
ant
8.2.
2.W
hat
is
mea
nt
by s
ucc
essi
ve t
erm
s? te
rms
that
co
me
on
e ri
gh
t af
ter
the
oth
er
3.C
ompl
ete
the
tabl
e.
Pat
tern
Is t
he
seq
uen
ce in
crea
sin
gIs
th
ere
a co
mm
on
dif
fere
nce
?
or
dec
reas
ing
?If
so
,wh
at is
it?
a.2,
5,
8, 1
1, 1
4, …
incr
easi
ng
yes;
3
b.
55,
50,
45,
40,
…d
ecre
asin
gye
s;�
5
c.1,
2,
4, 9
, 16
, …
incr
easi
ng
no
d.
, 0,
�,
�1,
…d
ecre
asin
gye
s;�
e.2.
6, 2
.9,
3.2,
3.5
, …
incr
easi
ng
yes;
0.3
Hel
pin
g Y
ou
Rem
emb
er
4.U
se t
he
patt
ern
3,7
,11,
15,…
to
expl
ain
how
you
wou
ld h
elp
som
eon
e el
se l
earn
how
to
fin
d th
e 10
th t
erm
of
an a
rith
met
ic s
equ
ence
.F
ind
th
e co
mm
on
dif
fere
nce
of
4.To
fin
d t
he
10th
ter
m,u
se t
he
form
ula
an
�a 1
�(n
�1)
d.S
ub
stit
ute
10
for
n,3
fo
r a 1
,an
d 4
fo
r d
.Th
e 10
th t
erm
is 3
9.
1 � 21 � 2
1 � 2
©G
lenc
oe/M
cGra
w-H
ill25
4G
lenc
oe A
lgeb
ra 1
Ari
thm
etic
Ser
ies
An
arit
hmet
ic s
erie
s is
a s
erie
s in
whi
ch e
ach
term
aft
er t
he f
irst
may
be
foun
d by
add
ing
the
sam
e nu
mbe
r to
the
pre
cedi
ng t
erm
.Let
Sst
and
for
the
foll
owin
g se
ries
in
whi
ch e
ach
term
is
3 m
ore
than
the
pre
cedi
ng o
ne.
S�
2 �
5 �
8 �
11 �
14 �
17 �
20
Th
e se
ries
rem
ain
s th
e sa
me
if w
e S
�2
�5
�8
�11
�14
�17
�20
reve
rse
the
orde
r of
all
th
e te
rms.
So
S�
20 �
17 �
14 �
11 �
8 �
5 �
2le
t u
s re
vers
e th
e or
der
of t
he
term
s 2S
�22
�22
�22
�22
�22
�22
�22
and
add
one
seri
es t
o th
e ot
her
,ter
m
2S�
7(22
)by
ter
m.T
his
is
show
n a
t th
e ri
ght.
S�
�7(
11)
�77
Let
are
pres
ent
the
firs
t te
rm o
f th
e se
ries
.L
et �
repr
esen
t th
e la
st t
erm
of
the
seri
es.
Let
nre
pres
ent
the
nu
mbe
r of
ter
ms
in t
he
seri
es.
In t
he
prec
edin
g ex
ampl
e,a
�2,
l �
20,a
nd
n�
7.N
otic
e th
at w
hen
you
add
the
two
seri
es,t
erm
by
term
,the
sum
of
each
pai
r of
ter
ms
is 2
2.T
hat
su
m c
an b
e fo
un
d by
add
ing
the
firs
t an
d la
st t
erm
s,2
�20
or
a�
�.N
otic
e al
so t
hat
th
ere
are
7,or
n,s
uch
su
ms.
Th
eref
ore,
the
valu
eof
2S
is 7
(22)
,or
n(a
��)
in
th
e ge
ner
al c
ase.
Sin
ce t
his
is
twic
e th
e su
mof
th
e se
ries
,you
can
use
th
e fo
llow
ing
form
ula
to
fin
d th
e su
m o
f an
yar
ith
met
ic s
erie
s.
S�
Fin
d t
he
sum
:1 �
2 �
3 �
4 �
5 �
6 �
7 �
8 �
9
a�
1,�
�9,
n�
9,so
S�
��
45
Fin
d t
he
sum
:�9
�(�
5) �
(�1)
�3
�7
�11
�15
a�
29,�
�15
,n�
7,so
S�
��
21
Fin
d t
he
sum
of
each
ari
thm
etic
ser
ies.
1.3
�6
�9
�12
�15
�18
�21
�24
108
2.10
�15
�20
�25
�30
�35
�40
�45
�50
270
3.�
21 �
(�16
) �
(�11
) �
(�6)
�(�
1) �
4 �
9 �
14�
28
4.ev
en w
hol
e n
um
bers
fro
m 2
th
rou
gh 1
0025
50
5.od
d w
hol
e n
um
bers
bet
wee
n 0
an
d 10
025
00
7 �
6�
27(
�9
�15
)�
� 2
9 �
10�
29(
1 �
9)�
� 2
n(a
��)
�� 2
7(22
)�
2
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-7
4-7
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Answers (Lesson 4-7)
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Wri
tin
g E
qu
atio
ns
fro
m P
atte
rns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-8
4-8
©G
lenc
oe/M
cGra
w-H
ill25
5G
lenc
oe A
lgeb
ra 1
Lesson 4-8
Loo
k fo
r Pa
tter
ns
A v
ery
com
mon
pro
blem
-sol
vin
g st
rate
gy i
s to
loo
k f
or a
pat
tern
.A
rith
met
ic s
equ
ence
s fo
llow
a p
atte
rn,a
nd
oth
er s
equ
ence
s ca
n f
ollo
w a
pat
tern
.
Fin
d t
he
nex
t th
ree
term
s in
th
e se
qu
ence
3,9
,27,
81,…
.
Stu
dy t
he
patt
ern
in
th
e se
quen
ce.
Su
cces
sive
ter
ms
are
fou
nd
bym
ult
iply
ing
the
last
giv
en t
erm
by
3.
Th
e n
ext
thre
e te
rms
are
243,
729,
2187
.
81
� 3
� 3
� 3
243
729
2187
3
� 3
� 3
� 3
927
81
Fin
d t
he
nex
t th
ree
term
sin
th
e se
qu
ence
10,
6,11
,7,1
2,8,
….
Stu
dy t
he
patt
ern
in
th
e se
quen
ce.
Ass
um
e th
at t
he
patt
ern
con
tin
ues
.
Th
e n
ext
thre
e te
rms
are
13,9
,14.
8
� 5
� 4
� 5
139
14
� 4
� 5
106
11
� 4
� 5
712
� 4
8
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
1.G
ive
the
nex
t tw
o it
ems
for
the
patt
ern
bel
ow.
Giv
e th
e n
ext
thre
e n
um
ber
s in
eac
h s
equ
ence
.
2.2,
12,7
2,43
2,…
3.
7,�
14,2
8,�
56,…
2592
,15,
552,
93,3
1211
2,�
224,
448
4.0,
10,5
,15,
10,…
5.
0,1,
3,6,
10,…
20,1
5,25
15,2
1,28
6.x
�1,
x�
2,x
�3,
…
7.x,
,,
,…
x�
4,x
�5,
x�
6,
,x � 7
x � 6x � 5
x � 4x � 3
x � 2
©G
lenc
oe/M
cGra
w-H
ill25
6G
lenc
oe A
lgeb
ra 1
Wri
te E
qu
atio
ns
Som
etim
es a
pat
tern
can
lea
d to
a g
ener
al r
ule
th
at c
an b
e w
ritt
en a
san
equ
atio
n.
Su
pp
ose
you
pu
rch
ased
a n
um
ber
of
pac
kag
es o
f b
lan
k c
omp
act
dis
ks.
If e
ach
pac
kag
e co
nta
ins
3 co
mp
act
dis
ks,
you
cou
ld m
ake
a ch
art
to s
how
the
rela
tion
ship
bet
wee
n t
he
nu
mb
er o
f p
ack
ages
of
com
pac
t d
isk
s an
d t
he
nu
mb
er o
f d
isk
s p
urc
has
ed.U
se x
for
the
nu
mb
er o
f p
ack
ages
an
d y
for
the
nu
mb
er o
f co
mp
act
dis
ks.
Mak
e a
tabl
e of
ord
ered
pai
rs f
or s
ever
al p
oin
ts o
f th
e gr
aph
.
Th
e di
ffer
ence
in
th
e x
valu
es i
s 1,
and
the
diff
eren
ce i
n t
he
yva
lues
is
3.T
his
pat
tern
show
s th
at y
is a
lway
s th
ree
tim
es x
.Th
is s
ugg
ests
th
e re
lati
on y
�3x
.Sin
ce t
he
rela
tion
is
also
a f
un
ctio
n,w
e ca
n w
rite
th
e eq
uat
ion
in
fu
nct
ion
al n
otat
ion
as
f(x)
�3x
.
1.W
rite
an
equ
atio
n f
or t
he
fun
ctio
n i
n2.
Wri
te a
n e
quat
ion
for
th
e fu
nct
ion
in
fun
ctio
nal
not
atio
n.T
hen
com
plet
e fu
nct
ion
al n
otat
ion
.Th
en c
ompl
ete
the
tabl
e.th
e ta
ble.
f(x
) �
4x�
2f(
x)
��
3x�
4
3.W
rite
an
equ
atio
n i
n f
un
ctio
nal
not
atio
n.
4.W
rite
an
equ
atio
n i
n f
un
ctio
nal
not
atio
n.
f(x
) �
�x
�2
f(x
) �
2x�
2
x
y Ox
y
O
x�
2�
10
12
3
y10
74
1�
2�
5x
�1
01
23
4
y�
22
610
1418
Nu
mb
er o
f P
acka
ges
12
34
5
Nu
mb
er o
f C
Ds
36
912
15
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Wri
tin
g E
qu
atio
ns
fro
m P
atte
rns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-8
4-8
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 4-8)
© Glencoe/McGraw-Hill A24 Glencoe Algebra 1
Skil
ls P
ract
ice
Wri
tin
g E
qu
atio
ns
fro
m P
atte
rns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-8
4-8
©G
lenc
oe/M
cGra
w-H
ill25
7G
lenc
oe A
lgeb
ra 1
Lesson 4-8
Fin
d t
he
nex
t tw
o it
ems
for
each
pat
tern
.Th
en f
ind
th
e 19
th f
igu
re i
n t
he
pat
tern
.
1. 2. Fin
d t
he
nex
t th
ree
term
s in
eac
h s
equ
ence
.
3.1,
4,10
,19,
31,…
46,6
4,85
4.15
,14,
16,1
5,17
,16,
…18
,17,
19
5.29
,28,
26,2
3,19
,…14
,8,1
6.2,
3,2,
4,2,
5,…
2,6,
2
7.x,
x�
1,x
�2,
…x
�3,
x�
4,x
�5
8.y,
4y,9
y,16
y,…
25y,
36y,
49y
Wri
te a
n e
qu
atio
n i
n f
un
ctio
n n
otat
ion
for
eac
h r
elat
ion
.
9.10
.11
.
f(x
) �
�2x
f(x
) �
x�
2f(
x)
�1
�x
12.
13.
14.
f(x
) �
x�
6f(
x)
�5
�x
f(x
) �
2x�
1
x
y
O
x
y
Ox
y
O
x
y
Ox
y
Ox
y
O
;;
©G
lenc
oe/M
cGra
w-H
ill25
8G
lenc
oe A
lgeb
ra 1
1.G
ive
the
nex
t tw
o it
ems
for
the
patt
ern
.Th
en f
ind
the
21st
fig
ure
in
th
e pa
tter
n.
Fin
d t
he
nex
t th
ree
term
s in
eac
h s
equ
ence
2.�
5,�
2,�
3,0,
�1,
2,1,
4,…
3,6,
53.
0,1,
3,6,
10,1
5,…
21,2
8,36
4.0,
1,8,
27,…
64,1
25,2
165.
3,2,
4,3,
5,4,
…6,
5,7
6.a
�1,
a�
4,a
�9,
…7.
3d�
1,4d
�2,
5d�
3,…
a�
16,a
�25
,a�
366d
�4,
7d�
5,8d
�6
Wri
te a
n e
qu
atio
n i
n f
un
ctio
n n
otat
ion
for
eac
h r
elat
ion
.
8.9.
10.
f(x
) �
�x
f(x
) �
3x�
6f(
x)
�2x
�4
BIO
LOG
YF
or E
xerc
ises
11
and
12,
use
th
e fo
llow
ing
info
rmat
ion
.
Mal
e fi
refl
ies
flas
h in
var
ious
pat
tern
s to
sig
nal l
ocat
ion
and
perh
aps
to w
ard
off
pred
ator
s.D
iffe
rent
spe
cies
of
fire
flie
s ha
ve d
iffe
rent
fla
sh c
hara
cter
isti
cs,s
uch
as t
he in
tens
ity
of t
hefl
ash,
its
rate
,and
its
shap
e.T
he t
able
bel
ow s
how
s th
e ra
te a
t w
hich
a m
ale
fire
fly
is f
lash
ing.
11.W
rite
an
equ
atio
n i
n f
un
ctio
n n
otat
ion
for
th
e re
lati
on.
f(t)
�2t
,wh
ere
tis
th
eti
me
in s
eco
nd
s an
d f
(t)
is t
he
nu
mb
er o
f fl
ash
es
12.H
ow m
any
tim
es w
ill
the
fire
fly
flas
h i
n 2
0 se
con
ds?
40
13.G
EOM
ETRY
Th
e ta
ble
show
s th
e n
um
ber
of d
iago
nal
s th
at c
an b
e dr
awn
fro
m o
ne
vert
ex i
n a
pol
ygon
.Wri
te a
neq
uat
ion
in
fu
nct
ion
not
atio
n f
or t
he
rela
tion
an
d fi
nd
the
nu
mbe
r of
dia
gon
als
that
can
be
draw
n f
rom
on
e ve
rtex
in
a
12-s
ided
pol
ygon
.f(
s) �
s�
3,w
her
e s
is t
he
nu
mb
er
of
sid
es a
nd
f(s
) is
th
e n
um
ber
of
dia
go
nal
s;9
Sid
es3
45
6
Dia
go
nal
s0
12
3
Tim
e (s
eco
nd
s)1
23
45
Nu
mb
er o
f F
lash
es2
46
810
1 � 2
x
y O
x
y
O
x
y
O
;
Pra
ctic
e (
Ave
rag
e)
Wri
tin
g E
qu
atio
ns
fro
m P
atte
rns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-8
4-8
Answers (Lesson 4-8)
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csW
riti
ng
Eq
uat
ion
s F
rom
Pat
tern
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-8
4-8
©G
lenc
oe/M
cGra
w-H
ill25
9G
lenc
oe A
lgeb
ra 1
Lesson 4-8
Pre-
Act
ivit
yW
hy
is w
riti
ng
equ
atio
ns
from
pat
tern
s im
por
tan
t in
sci
ence
?
Rea
d th
e in
trod
uct
ion
to
Les
son
4-8
at
the
top
of p
age
240
in y
our
text
book
.
•W
hat
is
mea
nt
by t
he
term
lin
ear
patt
ern
?T
he
po
ints
lin
e u
p a
lon
ga
stra
igh
t lin
e.
•D
escr
ibe
any
arit
hm
etic
seq
uen
ces
in t
he
data
.B
oth
th
e vo
lum
e o
fw
ater
an
d t
he
volu
me
of
ice
are
arit
hm
etic
seq
uen
ces.
Th
evo
lum
e o
f w
ater
has
a c
om
mo
n d
iffe
ren
ce o
f 11
an
d t
he
volu
me
of
ice
has
a c
om
mo
n d
iffe
ren
ce o
f 12
.
Rea
din
g t
he
Less
on
1.W
hat
is
mea
nt
by t
he
term
in
du
ctiv
e re
ason
ing?
mak
ing
a c
on
clu
sio
n b
ased
on
ap
atte
rn o
f ex
amp
les
2.F
or t
he
figu
res
belo
w,e
xpla
in w
hy
Fig
ure
5 d
oes
not
fol
low
th
e pa
tter
n.
If y
ou
fo
llow
th
e p
atte
rn o
f sh
adin
g t
he
top
tri
ang
le,t
hen
th
e b
ott
om
,th
en t
he
top
,an
d s
o o
n,F
igu
re 5
sh
ou
ld h
ave
the
top
tri
ang
le s
had
ed.
3.D
escr
ibe
the
step
s yo
u w
ould
use
to
fin
d th
e pa
tter
n i
n t
he
sequ
ence
1,5
,25,
125,
… .
Su
btr
act
succ
essi
ve t
erm
s to
fin
d o
ut
if it
is a
n a
rith
met
ic s
equ
ence
.It
isn
ot.
So
stu
dy
the
succ
essi
ve t
erm
s to
see
if m
ult
iplic
atio
n o
r d
ivis
ion
isu
sed
.Th
e p
atte
rn is
to
mu
ltip
ly e
ach
ter
m b
y 5
to g
et t
he
nex
t te
rm.
Hel
pin
g Y
ou
Rem
emb
er
4.W
hat
are
som
e ba
sic
thin
gs t
o re
mem
ber
wh
en y
ou a
re t
ryin
g to
dis
cove
r w
het
her
th
ere
is a
pat
tern
in
a s
equ
ence
of
nu
mbe
rs?
Sam
ple
an
swer
:L
oo
k to
see
wh
eth
ersu
cces
sive
ter
ms
incr
ease
or
dec
reas
e by
th
e sa
me
amo
un
t.If
no
t,lo
ok
to s
ee w
het
her
su
cces
sive
ter
ms
hav
e b
een
mu
ltip
lied
or
div
ided
by
the
sam
e n
um
ber
.
12
34
5
©G
lenc
oe/M
cGra
w-H
ill26
0G
lenc
oe A
lgeb
ra 1
Trac
eabl
e F
igu
res
Try
to
trac
e ov
er e
ach
of
the
figu
res
belo
w w
ith
out
trac
ing
the
sam
ese
gmen
t tw
ice.
Th
e fi
gure
at
the
left
can
not
be
trac
ed,b
ut
the
one
at t
he
righ
t ca
n.
Th
e ru
le i
s th
at a
fig
ure
is
trac
eabl
e if
it
has
no
poin
ts,o
r ex
actl
y tw
opo
ints
wh
ere
an o
dd n
um
ber
of s
egm
ents
mee
t.T
he
figu
re a
t th
e le
fth
as t
hre
e se
gmen
ts m
eeti
ng
at e
ach
of
the
fou
r co
rner
s.H
owev
er,t
he
figu
re a
t th
e ri
ght
has
exa
ctly
tw
o po
ints
,Lan
d Q
,wh
ere
an o
ddn
um
ber
of s
egm
ents
mee
t.
Det
erm
ine
wh
eth
er e
ach
fig
ure
can
be
trac
ed.I
f it
can
,th
enn
ame
the
star
tin
g p
oin
t an
d n
um
ber
th
e si
des
in
th
e or
der
in
wh
ich
th
ey s
hou
ld b
e tr
aced
.
1.Ye
s;E
2.N
o
3.Ye
s;X
4.
Yes;
D
E
AB
C
DK
F
HJ
G
611
105
4
13
27
812
13
9
E
WX
Y
F
HG
6 11
5 4
13
27
8109
PV
T S
U R
AB
EC
D
65
41
3
2
AB C
D
K Q
M
JP
L
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
4-8
4-8
Answers (Lesson 4-8)
© Glencoe/McGraw-Hill A26 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. C
A
D
C
C
B
C
A
C
C
D
B
{(0, �3), (1, �2),(2, �1), (3, 0)}
B
C
A
B
C
C
C
C
A
B
A
B
D
C
B
A
B
D
A
C
Chapter 4 Assessment Answer Key Form 1 Form 2APage 261 Page 262 Page 263
(continued on the next page)See Students’ Work
© Glencoe/McGraw-Hill A27 Glencoe Algebra 1
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: �4m2 � 10m � 6
B
D
A
A
C
C
A
B
B
D
C
A
D
C
A
D
B
B
C
C
{(6, 2), (4, 0), (12, �4)}
B
A
A
D
B
B
C
D
Chapter 4 Assessment Answer KeyForm 2A (continued) Form 2BPage 264 Page 265 Page 266
An
swer
s
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
1.
2.
3.4–6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:
(3, �1), (�1, �1), (3, 3)
y
xO
y
xO
(3, 4.5)
(3, 0)
(2, 0)
(2, 3)(0, 3)
(0, 4.5)
3 in. by 4.5 in.
Sample answer:f(d ) � 0.04d
an
nO 1
51015
2 4 5
�10�15
an � �7n � 19;
36, 43, 50
yes; 3
25v2 � 15v � 2
8
not a function
function
y
xO
yes; 2x � 3y � �4
no
y
xO
{(�1, �5), (3, �3)}
Domain:{�5, �2, 1, 3, 7};Range: {0, 2, 3, 4}
X
1�2�5
7
43023
Y
translation
reflection
y
xO
B
AC
(2, �1); IV(�2, �3); III
(3, 1); I
Chapter 4 Assessment Answer KeyForm 2CPage 267 Page 268
{(�3, 2), (�3, �1),(0, 1), (4, 3)}; {(2, �3),(�1, �3), (1, 0), (3, 4)}
{(�2, 5), (�1, 3),(0, 1), (1, �1), (2, �3)}
1.
2.
3.
4–6.
7.
8.
9.
Domain:{�2, �1, 1, 4, 8};Range: {�5, 0, 3, 7}
10.
11.
12.
13.
14.15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:y
xO
(�2, 3) (4, 3)
(�2, �2) (4, �2)
(�2, �2)
y
xO
(3, 5)
(3, 0)
(1.2, 0)
(1.2, 2)(0, 2)
(0, 5)
1.2 in. by 2 in.
f(d) � 0.05d
an
nO 1
5101520253035
2 3 4 5 6 7
an � 9n � 6;
�13, �10, �7
yes; 4
t2 � 4t � 7
39
function
not a function
y
xO
yes; 4x � 2y � 0
no
y
xO
{(�3, 5), (�2, 3),(�1, 1), (0, �1), (1, �3)}
{(�3, �16), (5, 8)}
{(�3, 3), (�2, 0),(0, �1), (2, 1)}; {(3, �3),(0, �2), (�1, 0), (1, 2)}
X
8�2
14
70
�53�1
Y
dilation
rotation
y
xOA
C
B
(�2, �4); III(�1, 2); II
(2, 3); I
An
swer
s
© Glencoe/McGraw-Hill A29 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyForm 2DPage 269 Page 270
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
about 12 yrs
about 10�12
� yrs
V(t) � 2000 � 190t
an
n1
2
2 3 4 5 6 7�2�4�6�8
�10�12�14
an � 4n � 19
y � �1
yes; �12
�
�24p2 � 16p
function
not a function
y
xO
yes; 3x � 7y � �6
y
xO 2
5
{(�4, 18), (3, �6.5),(5, �13.5), (6, �17)}
{(�3, �5.4), (15, 9)}
Domain:{�2, �1, 3, 4, 6};Range: {�2, �1, 3}
X
4�2�1
6
�1
3
�23
Y
y
xO
N'
M'
P'
M
N
P
M�(1, 0 ), N�(�1, 2),P�(�2, �3);
dilation
y
xO
(–3, 1.5)
, –432( )
(0, �8)
© Glencoe/McGraw-Hill A30 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyForm 3Page 271 Page 272
{(�3, 4), (�2, 1), (�1, �4),(1, 1), (3, 4), (3, �3)};{(4, �3), (1, �2), (�4, �1),(1, 1), (4, 3), (�3, 3)}
�(�4, �36), ��1, �31�12
��,(2, �27), �3, �25�
12
��,(6, �21)�; �(�36, �4),
��31�12
�, �1�, (�27, 2),
��25�12
�, 3�, (�21, 6)�
Chapter 4 Assessment Answer KeyPage 273, Open-Ended Assessment
Scoring Rubric
© Glencoe/McGraw-Hill A31 Glencoe Algebra 1
Score General Description Specific Criteria
• Shows thorough understanding of the concepts of pointson the coordinate plane, transformations, relations,functions, linear equations, arithmetic sequences, andpatterns.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of points on thecoordinate plane, transformations, relations, functions,linear equations, arithmetic sequences, and patterns.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts of pointson the coordinate plane, transformations, relations,functions, linear equations, arithmetic sequences, andpatterns.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts ofpoints on the coordinate plane, transformations, relations,functions, linear equations, arithmetic sequences, andpatterns.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
An
swer
s
© Glencoe/McGraw-Hill A32 Glencoe Algebra 1
Chapter 4 Assessment Answer KeyPage 273, Open-Ended Assessment
Sample Answers
1a. Sample answer: (�1, �1); quadrant III1b. Sample answer: (1, �1);
1c. The student should explain thatknowing in which quadrant a point is located determines whether the pointis to the right or left of the y-axis and above or below the x-axis,and thus, positive or negative.
2a. The four transformations are reflection,translation, dilation, and rotation.Depending on which two were chosen,the students may discuss whether theimage and preimage are the same size,whether a line or point was used toassist the movement of the figure,whether the movement preserved theorientation or reversed the orientationof the figure.
2b. The student should discuss thecharacteristics of the twotransformations that are the same. Thestudent should discuss whether thetransformations preserve size, direction,and orientation.
3a. Sample answer:{(�1, �3), (0, �1), (1, 4), (2, 5)};{(�3, �1), (�1, 0), (4, 1), (5, 2)}
3b. Sample answer:
3c. The student should identify in theirrelation where they used the samedomain element with two or moredifferent range elements.
4. Sample answer: x � y � 1; To graph theequation find two solutions for theequation, plot the two points associatedwith the two solutions, and draw astraight line through the two points.
5. The value in the range that correspondsto the element 2 in the domain isrepresented by f(2). The value f(2) isfound by substituting 2 for x in theequation.
6a.Sample answer: 2, 5, 8, 11, … ;The common difference is 3; a6 � 17
6b.Sample answer: 5, 3, 8, 6, 11, 9, 14, … ;The pattern is to subtract 2 from thefirst term to find the second term, thenadd 5 to the second term to find thethird term. Repeat the process ofsubtracting 2 then adding 5.
6c. The sequence 1, 1, 1, 1, … is a set ofnumbers whose difference betweensuccessive terms is the constant number0. Thus, this sequence is an arithmeticsequence by the definition.
X
�3�1
45
�1012
Y
y
xO
y
xO
(�1, �1) (1, �1)
In addition to the scoring rubric found on page A31, the following sample answers may be used as guidance in evaluating open-ended assessment items.
x y
�1 �3
0 �3
0 �1
1 4
2 5
© Glencoe/McGraw-Hill A33 Glencoe Algebra 1
1. axes
2. origin
3. quadrants
4. Transformations
5. translation
6. inverse
7. linear equation
8. function
9. vertical line test
10. the planecontaining the x- and y-axes
11. a diagram that usesarrows to show howthe elements of thedomain of a relationare paired withelements of therange
1.
2.
3.
4.
5.
Quiz (Lessons 4–3 and 4–4)
Page 275
1.
Domain: {�4, 1, 2, 3} Range: {3, 4, 5, 6, 8}
2.
3.
4.
5.
1.
2.
3.
4.
5.
Quiz (Lessons 4–7 and 4–8)
Page 276
1.
2.
3.
4.
5. f(x) � 2x � 2
5, 1, �15
�
25
21, 25, 29
no
B
30
function
y
xO
yes; 2x � y � 1
{(�3, �2), (�2, 0),(�1, 2), (0, 4), (1, 6)}
{(�2, 0), (�1, 1.5),(0, 3), (2, 6), (3, 7.5)}
{(�2, �11), (2, 5)}
{(�5, 2), (�3, �2),(1, 1), (4, �3};{(2, �5), (�2, �3),(1, 1), (�3, 4)}
X
56843
3�4
21
Y
y
xO
A'
B'
C'
A
B
C
A�(�1, 2), B�(�3, 3),C� (�3, �1)
dilation
rotation
(2, �4); IV
(�3, 0); none
Chapter 4 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 4–1 and 4–2) Quiz (Lessons 4–5 and 4–6)
Page 274 Page 275 Page 276
An
swer
s
© Glencoe/McGraw-Hill A34 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14. y
xO
{(�3, �17), (�1, �9),(1, �1), (2, 3), (5, 15)}
y
xAA�
B
B�
C
C�
A�(�1, 0), B�(2, �4),C�(3, �1)
not a function
{(�4, 3), (�4, �1),(�2, 2), (0, �1), (2, 3),(3, �3), (4, 1)}; domain:{�4, �2, 0, 2, 3, 4};range: {�3, �1, 1, 2, 3}
(�4, 3); II
no
�2
$12.75
x divided by 4 minus yequals negative 2 times
the quotient of x and y.
6.16
8m � 9n
�45
�
{(�3, 1), (0, 2),(3, 3), (6, 4)}:
{(�2, �7), (�1, �5),(0, �3), (2, 1), (3, 3)}
D�(1, 1), E�(4, 1), F�(2, 4);
X
�2
�1
0
�3357
Y
B
D
A
B
C
Chapter 4 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 277 Page 278
Stem Leaf0 5 81 0 2 2 2 2 2 52 0
1�0 � 10
See students’ graphs.
© Glencoe/McGraw-Hill A35 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 12.
13. 14.
15.
16.
17. DCBA
DCBA
DCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
7 7
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
1 4
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
2 8
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
3 7
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
Chapter 4 Assessment Answer KeyStandardized Test Practice
Page 279 Page 280
An
swer
s