Chapter 6 and 7 Practice Test - Ms Jeong Webpage -...

Chapter 6 and 7 Practice Test

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Which set of ordered pairs does not represent a function?

i)

ii)

iii)

iv)

a. i b. ii c. iv d. iii

____ 2. Identify the domain of this relation.

a. c.

b. d.

____ 3. Identify the range of this relation.

1

3

6

8

9

–2

0

3

5

a. c.

b. d.

____ 4. For the function , determine .

a. 7 b. 2 c. 14 d. 3

____ 5. For the function , determine x when .

a. 83 b. –67 c. 11 d. –11

____ 6. Write as an equation in two variables. a. c. b. d.

____ 7. Joshua went on a bike ride. During the ride, he stopped to play at a park, as shown by line segment CD. How much time did Joshua spend at the park?

Time (min)

Dis

tan

ce f

rom

ho

me (

km

)

Joshua's Bike Ride

O

A

B

C D

E

20 40 60 80 100 120

1

2

3

4

5

a. 65 min. b. 75 min. c. 70 min. d. 80 min.

____ 8. A person in a car drives away from a stop sign, cruises at a constant speed, and then slows down as she approaches another stop sign. Which graph best represents this situation?

a.

Time (min)

Sp

eed

(km

/h)

c.

Time (min)

Sp

eed

(km

/h)

b. d.

Time (min)

Sp

eed

(km

/h)

Time (min)

Sp

eed

(km

/h)

____ 9. This graph shows the free-fall speed of a skydiver as a function of time. At what speed was the skydiver travelling 10 s before she reached the ground?

Time (s)

Sp

eed

(km

/h)

Free-Fall Speed of a Skydiver

O

A B

C

D

E

5 10 15 20 25 30 35 40 45 50 55 60 65

40

80

120

160

a. 20 km/h b. 140 km/h c. 30 km/h d. 10 km/h

____ 10. Which graph best represents the cost of renting a kayak as a function of time?

a. c.

Time (h)

Co

st

($)

Renting a Kayak

Time (h)

Co

st

($)

Renting a Kayak

b.

Time (h)

Co

st

($)

Renting a Kayak

d.

Time (h)

Co

st

($)

Renting a Kayak

____ 11. Which of these graphs represents a function? i) ii)

x

y

x

y

iii) iv)

x

y

x

y

a. ii b. i c. iii d. iv

____ 12. Which of these graphs represents a function? i) ii)

x

y

x

y

iii) iv)

x

y

x

y

a. iv b. ii c. i d. iii

____ 13. Determine the domain and range of the graph of this function.

y = f(x)

0 2 4–2–4 x

2

4

–2

–4

–6

y

a. c.

b. d.

____ 14. This graph shows the masses of people, m, as a function of age, a. Determine the range of the graph.

Age (years)

Mass (

kg

)

Ages and Masses of People

0 4 8 12 16 20 a

20

40

60

80

100m

a. c.

b. d.

____ 15. This is a graph of the function . Determine the range value when the domain value is 2.

g(x) = –2x + 3

0 2 4–2–4 x

2

4

–2

–4

y

a. 0.5 b. 7 c. –1 d. 1

____ 16. This is a graph of the function . Determine the domain value when the range value is –4.

g(x) = –3x + 2

0 2 4–2–4 x

2

4

–2

–4

y

a. –2 b. 0.5 c. 11 d. 2

____ 17. This graph represents a 150-L hot-water tank being filled at a constant rate. Determine the rate of change of the relation.

Time (min)

Vo

lum

e (

L)

Filling a Hot-Water Tank

(25, 75)

(50, 150)

0 10 20 30 40 50 t

25

50

75

100

125

150

175V

a. 25 L/min c. 75 L/min b. 3 L/min d. 0.33 L/min

____ 18. Which equation does not represent a linear relation?

i)

ii) iii)

iv)

a. iii b. ii c. i d. iv

____ 19. This graph shows distance, d kilometres, as a function of time, t minutes. Determine the vertical and horizontal intercepts.

Time (min)

Dis

tan

ce (

km

)

d = f(t)

20 40 60 80 100 120 t

20

40

60

80

100

d

a. Vertical intercept: 80

Horizontal intercept: 96

c. Vertical intercept: 96 Horizontal intercept: 80

b. Vertical intercept: 64 Horizontal intercept: 96

d. Vertical intercept: 80 Horizontal intercept: 64

____ 20. Which graph represents the linear function ?

a.

0 2 4–2–4 x

2

4

–2

–4

y

c.

0 2 4–2–4 x

2

4

–2

–4

y

b. d.

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

____ 21. The graph shows the cost of hosting an anniversary party. What is the maximum number of people who can attend the party for a cost of $1500?

Cost of an Anniversary Party

Co

st

($)

Number of people

010 20 30 40 50 60 n

300

600

900

1200

1500

1800

2100

C

a. 61 people c. 33 people b. 38 people d. 27 people

____ 22. This graph shows the cost of a taxi ride. The cost, C dollars, is a function of the duration of the ride, t min. What is the duration of the ride when the cost is $35?

Time (min)

Co

st

($)

Cost of a Taxi Ride

010 20 30 40 50 60 70 t

10

20

30

40

50

C

a. 45 min c. 50 min b. 58 min d. 53 min

____ 23. Determine the slope of this line segment.

0

A

B

2 4–2–4 x

2

4

–2

–4

y

a.

−

2

3

c. 2

3

b. −

3

2

d. 3

2

____ 24. Determine the slope of the line that passes through G(3, –3) and H(–5, 9).

a. 3

2

c. 2

3

b. −

2

3

d. −

3

2

____ 25. Is the slope of this line segment positive, negative, zero, or not defined?

0

S

T

4 8–4–8 x

4

8

–4

–8

y

a. zero c. not defined b. positive d. negative

____ 26. Determine the steepness of this roof by calculating its slope.

rise

run

a.

−

5

3

c. 3

5

b. 5

3

d. −

3

5

____ 27. A straight section of an Olympic downhill ski course is 34 m long. It drops 16 m in height. Determine the slope of this part of the course. a.

c.

b.

d.

____ 28. A line has x-intercept 2 and y-intercept 6? Determine the slope of the line. a. 1

3

c. −3

b. 3 d. −

1

3

____ 29. Which of these line segments are parallel?

0A

B

E

F

C

D

G

H

2 4–2–4 x

2

4

–2

–4

y

a. CD and EF c. AB and CD b. EF and GH d. AB and EF

____ 30. Determine the slope of the line that is perpendicular to this line segment.

0

A

B

2 4–2–4 x

2

4

–2

–4

y

a. 3 c. 1

3

b. –3 d. –

1

3

____ 31. Determine the slope of the line that is parallel to this line segment.

0

K

X

2 4–2–4 x

2

4

–2

–4

y

a.

–3

7

c. 3

7

b. 7

3

d. –

7

3

____ 32. Determine the slope of a line that is perpendicular to the line through W(–9, 7) and X(6, –10). a.

−

15

17

c. –15

b. −

17

15

d. 15

17

____ 33. Determine the slope of a line that is parallel to the line through L(–6, 3) and K(12, –9). a. 2

3

c. −

2

3

b. 3

2

d. −

3

2

____ 34. Write an equation for the graph of a linear function that has slope and y-intercept –3.

a.

c.

b.

d.

____ 35. Which graph represents the equation ?

a. c.

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 36. For a service call, a plumber charges a $95 initial fee, plus $45 for each hour he works. Write an equation to represent the total cost, C dollars, for t hours of work. a. c. b. d.

____ 37. Which graph has slope 1 and y-intercept 0?

a. c.

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 38. Describe the graph of the linear function with this equation:

a. The graph is a line through (–2, 3) with slope .

b. The graph is a line through (2, ) with slope .

c. The graph is a line through (2, ) with slope .

d. The graph is a line through (–2, 3) with slope .

____ 39. Write an equation for the graph of a linear function that has slope 8 and passes through R(4, ). a.

b.

c.

d.


a.

0 2 4–2–4 x

2

4

–2

–4

y

c.

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 41. Write an equation in slope-point form for this line.

0 2 4–2–4 x

2

4

–2

–4

y

a.

c.

b.

d.

____ 42. Write this equation in slope-intercept form:

a.

13

5

c.

13

5

b.

13

5

d.

13

5

____ 43. Determine the y-intercept of the graph of this equation:

a. c. b. 13 d. 3

____ 44. Write an equation in slope-point form for the line that passes through A(1, 4) and B(6, 8). a.

c.

b.

d.

____ 45. Write this equation in general form:

a. c.

b. d.

____ 46. Write this equation in general form:

a. c.

b. d.

____ 47. Determine the x-intercept and the y-intercept for the graph of this equation:

a. x-intercept: 18; y-intercept: 12 c. x-intercept: 18; y-intercept: b. x-intercept: ; y-intercept: d. x-intercept: ; y-intercept: 12

____ 48. Which equation is written in general form? a. c.

b. d.


a. c.

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 50. Write this equation in slope-intercept form:

a. y =

10

3x +

4

3

c. y =

10

3x –

4

3

b. y = –

10

3x +

4

3

d. y = –

10

3x – 4

____ 51. Which equation is equivalent to ?

a.

c.

b.

d.

____ 52. A line has x-intercept –9 and y-intercept 3. Determine the equation of the line in general form. a. c.

b. d.

____ 53. Jon has x egg cartons that hold 12 eggs and y egg cartons that hold 18 eggs. He uses these cartons to store 72 eggs. Which equation represents the relation? a. c.

b. d.

Short Answer

54. Consider the relation represented by this set of ordered pairs.

Describe the relation in words.

55. Different coloured game pieces can be associated with their lengths, in centimetres. Consider the relation

represented by this arrow diagram. Represent the relation as a graph.

Red

Black

Yellow

Green

White

5

7

10

12

has a length (cm) of

Blue

56. For the function , determine .

57. For the function , determine x when .

58. a) Write in function notation:

b) Write as an equation in two variables:

59. Natasha spent part of the afternoon running errands. This graph shows her distance from home as a function

of time.

Time (min)

Dis

tan

ce f

rom

ho

me (

km

)

Natasha's Drive

O

A

B

C D

E

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115

1

2

3

4

5

6

7

8

a) How far did Natasha drive in total? b) How long was Natasha away from home?

60. This table shows the refund, r dollars, for different numbers of juice tetra paks, n. Is this relation a function?

Explain.

Number of Juice Tetra Paks, n

Refund, r ($)

5 0.25

12 0.60

17 0.85

24 1.20

30 1.50

61. Which equations represent linear relations? Create tables of values if necessary.

a) d)

b) e)

c) f)

62. Determine the vertical and horizontal intercepts of this graph.

0

y = f(x)

2 4–2–4 x

2

4

–2

–4

y

63. Determine the rate of change and the vertical intercept of this graph.

0

y = f(x)

2 4–2–4 x

2

4

–2

–4

y

64. This graph shows the cost, C dollars, of printing an advertising flyer for the school play as a function of the

number of flyers printed, n. What is the cost when 1000 flyers are printed?

Number of flyers (100s)

Co

st

($)

Flyers for the School Play

0 4 8 12 16 20 n

100

200

300

400

500 C

65. This graph shows cost, C dollars, as a function of time, t hours. What is the time when the cost is $35?

Time (h)

Co

st

($)

0

C = f(t)

1 2 3 4 t

10

20

30

40

50

60

C

66. A line has x-intercept –8 and y-intercept 5. Determine the slope of a line perpendicular to this line.

67. For each equation, identify the slope and y-intercept of its graph.

i)

ii)

iii)

68. Write an equation for the line that passes through E(–3, –7) and F(2, 10). Write the equation in slope-point

form and in slope-intercept form.

69. Write this equation in general form:

70. Determine the slope of the line of this equation:

Problem

71. A relation contains 5 elements in the domain and 6 elements in the range. Can this relation be a function?

Justify your answer.

72. A gas station attracts customers by offering coupons worth $0.03 for every $1.00 spent on gasoline.

Value of Gas Purchase, v

($)

Value of Coupons, c

($)

1

2

0.36

20

1.20

50

a) Use function notation to express c as a function of v. b) Copy and complete the table. c) What is the value of the coupons a customer will receive if she spends $80 on gasoline? d) How much does a customer have to spend on gasoline to receive $5.00 in coupons?

73. This table shows the speed of a hot air balloon at different time intervals after lift off. A student drew a graph

to represent the data in the table.

Time, t (s)

Speed, S (m/s)

0 0

1 2.4

2 5.6

3 10.0

4 12.4

6 15.0

9 16.1

10 16.1

Time (s)

Sp

eed

(m

/s)

Speed of a Hot Air Balloon

2 4 6 8 10

5

10

15

20

25

a) Describe any errors in the graph. b) Is this relation a function? Explain.

74. Four litres of latex paint covers approximately 37 m2 and costs $52.

a) Copy and complete this table.

Volume of Paint, p (L) 0 4 8 12 16

Cost, c ($) 0 52

Area Covered, A (m2) 0 37

b) Graph the area covered as a function of the volume of paint.

c) Graph the area covered as a function of the cost.

d) Write the domain and range of the functions in parts b and c.

75. a) This is a graph of the function .

Determine the range value when the domain value is 2.

f(x) = 2 x + 1

0 2 4–2–4 x

2

4

–2

–4

y

b) This is the graph of the function .

Determine the range value when the domain value is 3.

g(x) = 1 – 2x

0 2 4–2–4 x

2

4

–2

–4

y

76. A company rents paddle boats by the day. This table shows the total cost of renting a paddle boat for different

numbers of days.

Number of Days (n)

Total Cost ($)

1 $54.00

3 $112.00

5 $170.00

7 $228.00

a) Graph the relation between the total cost of the rental and the number of days.

b) Does the graph represent a linear relation? How do you know? c) Determine the rate of change, then describe what it represents.

77. The graph represents the cost of printing pamphlets.

Number of pamphlets (hundreds)

Co

st

($)

Cost of Printing Pamphlets

04 8 12 16 20 n

60

120

180

240

300

360

c

a) Identify the dependent and independent variables. b) Sohan calculated the rate of change as follows:

Change in cost:

Change in number of pamphlets: 2000 pamphlets – 500 pamphlets = 1500 pamphlets

Rate of change:

Did he calculate the rate of change correctly? Explain.

c) Describe what the rate of change represents.

78. This graph represents the relation between the distance a vehicle travels and the number of revolutions of a

tire. An equation for the distance travelled, d metres, after r revolutions of the tire is .

Distance a Car Travels

Dis

tan

ce (

m)

Number of tire revolutions

0100 200 300 400 500 600 700 r

200

400

600

800

1000

1200

1400

1600d

a) Identify the dependent and independent variables. b) Does the graph represent a linear relation? How do you know? c) Describe another strategy you could use to determine whether this relation is linear.

79. This graph shows the length, l metres, of an object’s shadow as a function of the height of the object, h

metres.

Height of object (m)

Len

gth

of

sh

ad

ow

(m

)

Length of an Object's Shadow

04 8 12 16 20 24 28 32 36 h

10

20

30

40

50

60

70l

a) What is the rate of change? What does it represent? b) A tree has height 13 m. About how long is its shadow? c) The length of the shadow of a building is 45 m. About how tall is the building?

80. Sketch a graph of the linear function .

81. This graph shows the distance, d kilometres, from Beijing, China, to Edmonton, Alberta, as a function of

flying time, t hours.

Dis

tan

ce (

km

)

Time (h)

Flight from Beijing to Edmonton

0 2 4 6 8 10 12 t

1000

2000

3000

4000

5000

6000

7000

8000

9000d

a) Determine the vertical and horizontal intercepts. Write the coordinates of the points where the graph

intersects the axes. Describe what the points of intersection represent. b) Determine the rate of change. What does it represent? c) Write the domain and range? d) What is the distance to Edmonton when the plane has been flying for 5 h? e) How many hours has the plane been flying when the distance to Edmonton is 6500 km?

82. A guy wire helps to support a tower. One end of the wire is 25 m from the base of the tower. The wire has a

slope of 8

5. How high up the tower does the wire reach?

83. Four students determined the slope of the line through S(7, –5) and T(–15, 11). Their answers were: 11

8,

−

11

8,

8

11, and −

8

11.

Which answer is correct? How do you know?

84. Given A(18, 9), B(6, 27), and C(6, 9), determine the coordinates of point D such that CD is parallel to AB and

D is on the: i) y-axis ii) x-axis

85. A student said that the equation of this graph is .

a) What mistakes did the student make?

b) What is the equation of the graph?

0 2 4–2–4 x

2

4

–2

–4

y

86. An equation of a line is . Determine the value of m when the line passes through the point J(–5, 2).

87. Francine runs a T-shirt company. For each order she receives, Francine charges a flat fee of $50, plus $8.95

per T-shirt . a) Write an equation for the total cost, C dollars, for ordering n T-shirts. b) Marnell ordered 62 T-shirts. What was the total cost? c) Jakub paid a total cost of $971.85. How many T-shirts did he order?

88. Students at Tahayghen Secondary School sell punch during the school carnival. The number of cups sold, n,

is a linear function of the temperature in degrees Celsius, t. The students sold 458 cups when the temperature was 25°C. They sold 534 cups when the temperature was 29°C. a) Write an equation in slope-point form to represent this function. b) Use the equation in part a to determine the approximate temperature when the students sell 325 cups of

punch.

89. Write an equation in general form for the line that passes through A(3, –4) and B(11, 8).

90. Graph this equation:

Describe the strategies you used.

0 4 8 12 16–4–8–12–16 x

4

8

–4

–8

y

Chapter 6 and 7 Practice Test Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: Easy REF: 5.2 Properties of Functions

LOC: 10.RF2 TOP: Relations and Functions KEY: Conceptual Understanding

2. ANS: C PTS: 1 DIF: Easy REF: 5.2 Properties of Functions LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

3. ANS: C PTS: 1 DIF: Easy REF: 5.2 Properties of Functions LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

4. ANS: C PTS: 1 DIF: Easy REF: 5.2 Properties of Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Procedural Knowledge

5. ANS: C PTS: 1 DIF: Easy REF: 5.2 Properties of Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Procedural Knowledge

6. ANS: B PTS: 1 DIF: Easy REF: 5.2 Properties of Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Conceptual Understanding

7. ANS: C PTS: 1 DIF: Easy REF: 5.3 Interpreting and Sketching Graphs LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

8. ANS: D PTS: 1 DIF: Moderate REF: 5.3 Interpreting and Sketching Graphs LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

9. ANS: A PTS: 1 DIF: Easy REF: 5.3 Interpreting and Sketching Graphs LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

10. ANS: A PTS: 1 DIF: Easy REF: 5.3 Interpreting and Sketching Graphs LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

11. ANS: B PTS: 1 DIF: Easy REF: 5.5 Graphs of Relations and Functions LOC: 10.RF2 TOP: Relations and Functions KEY: Conceptual Understanding

12. ANS: A PTS: 1 DIF: Easy REF: 5.5 Graphs of Relations and Functions LOC: 10.RF2 TOP: Relations and Functions KEY: Conceptual Understanding

13. ANS: B PTS: 1 DIF: Easy REF: 5.5 Graphs of Relations and Functions LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

14. ANS: D PTS: 1 DIF: Easy REF: 5.5 Graphs of Relations and Functions LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

15. ANS: C PTS: 1 DIF: Easy REF: 5.5 Graphs of Relations and Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Conceptual Understanding

16. ANS: D PTS: 1 DIF: Easy REF: 5.5 Graphs of Relations and Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Conceptual Understanding

17. ANS: B PTS: 1 DIF: Easy REF: 5.6 Properties of Linear Functions

LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge

18. ANS: C PTS: 1 DIF: Moderate REF: 5.6 Properties of Linear Functions LOC: 10.RF4 TOP: Relations and Functions KEY: Procedural Knowledge

19. ANS: A PTS: 1 DIF: Easy REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding

20. ANS: A PTS: 1 DIF: Easy REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

21. ANS: C PTS: 1 DIF: Easy REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Conceptual Understanding

22. ANS: D PTS: 1 DIF: Easy REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Conceptual Understanding

23. ANS: B PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

24. ANS: D PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

25. ANS: C PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding

26. ANS: B PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

27. ANS: B PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

28. ANS: C PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

29. ANS: D PTS: 1 DIF: Easy REF: 6.2 Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge


31. ANS: C PTS: 1 DIF: Easy REF: 6.2 Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge


33. ANS: C PTS: 1 DIF: Easy REF: 6.2 Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge

34. ANS: B PTS: 1 DIF: Easy REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding


36. ANS: C PTS: 1 DIF: Easy

REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding


38. ANS: B PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

39. ANS: B PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

40. ANS: C PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

41. ANS: A PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

42. ANS: A PTS: 1 DIF: Moderate REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

43. ANS: B PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

44. ANS: C PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

45. ANS: A PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

46. ANS: C PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

47. ANS: D PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

48. ANS: B PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

49. ANS: C PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

50. ANS: B PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

51. ANS: C PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6

TOP: Relations and Functions KEY: Conceptual Understanding

52. ANS: C PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

53. ANS: A PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

SHORT ANSWER

54. ANS:

The relation shows the association “multiplied by 5 is” from a set of numbers to a set of numbers.

PTS: 1 DIF: Moderate REF: 5.1 Representing Relations LOC: 10.RF4 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

55. ANS:

Red

Bla

ck

Yello

w

Gre

en

White

Lengths of Game Pieces

Len

gth

(cm

)

Blu

e

0

1

2

3

4

5

6

7

8

9

10

11

12

Colour

PTS: 1 DIF: Moderate REF: 5.1 Representing Relations LOC: 10.RF4 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

56. ANS: –37

PTS: 1 DIF: Moderate REF: 5.2 Properties of Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Procedural Knowledge

57. ANS: –30

PTS: 1 DIF: Moderate REF: 5.2 Properties of Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Procedural Knowledge

58. ANS: a)

b)

PTS: 1 DIF: Easy REF: 5.2 Properties of Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Conceptual Understanding

59. ANS: a) 10 km b) 115 min

PTS: 1 DIF: Moderate REF: 5.3 Interpreting and Sketching Graphs LOC: 10.RF1 TOP: Relations and Functions KEY: Conceptual Understanding

60. ANS: For each number in the first column, there is only one number in the second column. So, the relation is a function.

PTS: 1 DIF: Easy REF: 5.4 Graphing Data LOC: 10.RF2 TOP: Relations and Functions KEY: Communication | Conceptual Understanding

61. ANS: The relations in parts a, c, and f are linear.

PTS: 1 DIF: Moderate REF: 5.6 Properties of Linear Functions LOC: 10.RF4 TOP: Relations and Functions KEY: Conceptual Understanding

62. ANS: Horizontal intercept: 3 Vertical intercept: 2

PTS: 1 DIF: Easy REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding

63. ANS: Rate of change: −1; vertical intercept: 2

PTS: 1 DIF: Easy REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

64. ANS: $200.00


65. ANS: 1.5 h


66. ANS:

–8

5

PTS: 1 DIF: Moderate REF: 6.2 Slopes of Parallel and Perpendicular Lines

LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge

67. ANS: i) slope: 5; y-intercept:

ii) slope: ; y-intercept: 9

iii) slope: ; y-intercept:

PTS: 1 DIF: Easy REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

68. ANS:

or

PTS: 1 DIF: Moderate REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge

69. ANS:

PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

70. ANS:

PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding

PROBLEM

71. ANS:

Sample answer: A relation is a function when each element in the domain is associated with exactly one element in the range. If there are more elements in the range than in the domain, at least one element in the domain is associated with more than one element in the range. This violates the definition of a function. Therefore, the relation is not a function.

For example:

A

B

C

D

E

3

1

2

4

5

6

PTS: 1 DIF: Difficult REF: 5.2 Properties of Functions LOC: 10.RF2 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

72. ANS: a)

b)

Value of Gas Purchase, v

($)

Value of Coupons, c

($)

1 0.03

2 0.06

12 0.36

20 0.60

40 1.20

50 1.50

c) To determine c(80), use:

c(80) is the value of c when . This means that when a customer spends $80 on gasoline, she will receive coupons valued at $2.40.

d) To determine the value of v when , use:

means that when , ; that is, a customer has to spend $166.67 on

gasoline to receive $5.00 in coupons.

PTS: 1 DIF: Difficult REF: 5.2 Properties of Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Problem-Solving Skills

73. ANS: a) Since time and speed can have any numerical value between those indicated by the points on the graph,

the points on the graph should be joined. b) The relation is a function because there is only one speed for each time.

PTS: 1 DIF: Moderate REF: 5.4 Graphing Data LOC: 10.RF1 | 10.RF2 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

74. ANS: a)

Volume of Paint, p (L) 0 4 8 12 16

Cost, c ($) 0 52 104 156 208

Area Covered, A (m2) 0 37 74 111 148

b)

Volume of paint (L)

Are

a c

overe

d (

m )2

Area Covered by Paint

0 4 8 12 16 p

20

40

60

80

100

120

140

160

A

c)Area that Can Be

Covered for a Given Cost

Cost ($)

Are

a c

overe

d (

m )2

0 50 100 150 200 c

20

40

60

80

100

120

140

160

A

d) Part b: domain: ; range:

Part c: domain: ; range:

PTS: 1 DIF: Difficult REF: 5.5 Graphs of Relations and Functions LOC: 10.RF1 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

75. ANS: a)

To determine the value of f(x) when : Begin at on the x-axis. Draw a vertical line to the graph, then a horizontal line to the y-axis. The line appears to intersect the y-axis at 5. So,

When the domain value is 2, the range value is 5.

f(x) = 2 x + 1

0 2 4–2–4 x

2

4

–2

–4

y

b)

To determine the value of x when :

Since , begin at on the

y-axis. Draw a horizontal line to the graph, then a vertical line to the x-axis. The line appears to intersect the x-axis at –1. So, when ,

When the range value is 3, the domain value is –1.

g(x) = 1 – 2x

0 2 4–2–4 x

2

4

–2

–4

y

PTS: 1 DIF: Moderate REF: 5.5 Graphs of Relations and Functions LOC: 10.RF8 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

76. ANS: a)

Number of days

Co

st

($)

Cost of Renting a Paddle Boat

0 1 2 3 4 5 6 7 n

40

80

120

160

200

240

c

b) This graph represents a linear relation because the points lie on a straight line. c) Choose two points on the line. Calculate the change in each variable from one point to the other.

Change in cost:

Change in number of days: 7 days – 3 days = 4 days

Rate of change:

The rate of change represents the daily cost of renting a paddle boat, which is $29.00 per day.

PTS: 1 DIF: Moderate REF: 5.6 Properties of Linear Functions LOC: 10.RF4 | 10.RF3 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

77. ANS: a) The dependent variable is the cost, c. The independent variable is the number of copies, n. b) No, Sohan did not calculate the rate of change correctly. Instead of dividing the change in the cost by the

change in the number of pamphlets, he divided the change in the number of pamphlets by the change in the cost.

Rate of change: $0.14/pamphlet

c) The rate of change represents the cost of printing each pamphlet after the machine has been set up. The

cost per pamphlet is 14¢.

PTS: 1 DIF: Moderate REF: 5.6 Properties of Linear Functions LOC: 10.RF4 | 10.RF3 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

78. ANS: a) The dependent variable is distance, d. The independent variable is number of tire revolutions, r.

b) The graph represents a linear relation because the graph is a straight line. c) I could create a table of values for the relation, then calculate the change in each variable. If the changes

in both variables are constant, the relation is linear.

PTS: 1 DIF: Moderate REF: 5.6 Properties of Linear Functions LOC: 10.RF4 | 10.RF3 | 10.RF1 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

79. ANS: a) Choose two points on the line. Calculate the change in each variable from one point to the other.

Change in length of shadow:

Change in height of object:

Rate of change:

The rate of change is positive so the length of the shadow increases with the height of the object. For every 1 m of height, the length of the shadow is 3 m.

b) To estimate the length of the shadow, use the graph.

From 13 on the h-axis, draw a vertical line to the graph, then a horizontal line to the l-axis. From the graph, the length of the shadow will be about 39 m.

c) To estimate the height of the building, use the graph.

From 45 on the l-axis, draw a horizontal line to the graph, then a vertical line to the h-axis. From the graph, the height of the building will be about 15 m.

PTS: 1 DIF: Moderate REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF3 | 10.RF8 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

80. ANS:

Since the function is linear, its graph is a straight line. Determine the y-intercept: When ,

Determine the x-intercept: When ,

Determine the coordinates of a third point on the graph. When ,

Plot the points (0, 2), (5, 0), and (10, –2), then draw a line through them.

0 2 4 6 8 10–2 x

2

4

6

–2

–4

–6

y

PTS: 1 DIF: Moderate REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF1 | 10.RF3 | 10.RF8 TOP: Relations and Functions KEY: Problem-Solving Skills

81. ANS: a) On the vertical axis, the point of intersection has coordinates (0, 9000). The vertical intercept is 9000. At

the start of the trip, the distance from Beijing to Edmonton is 9000 km. On the horizontal axis, the point of intersection has coordinates (12, 0). The horizontal intercept is 12. It takes approximately 12 h to fly from Beijing to Edmonton.

b) Choose two points on the line. Calculate the change in each variable from one point to the other.

Change in distance:

Change in time:

Rate of change:

The rate of change is negative so the distance is decreasing with time. Every hour, the distance to Edmonton decreases by approximately 750 km.

c) The domain is the set of possible values of the time:

The range is the set of possible values of the distance:

d) To estimate the distance to Edmonton, use the graph.

From 5 on the t-axis, draw a vertical line to the graph, then a horizontal line to the d-axis. From the graph, the distance to Edmonton is approximately 5250 km.

e) To estimate how many hours the plane has been flying, use the graph.

From 6500 on the d-axis, draw a horizontal line to the graph, then a vertical line to the t-axis. From the

graph, the number of hours the plane has been flying is approximately 3 h.

PTS: 1 DIF: Moderate REF: 5.7 Interpreting Graphs of Linear Functions LOC: 10.RF3 | 10.RF5 | 10.RF8 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

82. ANS: Sketch a diagram.

rise

25 m

The guy wire is attached to the building 40 m above the ground.

PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Problem-Solving Skills

83. ANS: Subtract corresponding coordinates to determine the change in x and in y. From S to T: The rise is the change in y-coordinates.

The run is the change in x-coordinates.

Slope of ST = −

8

11

The slope of ST is −

8

11.

The correct answer is −

8

11.

PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

84. ANS:

Slope of AB =

Slope of AB =

Slope of AB =

The slope of AB is −

3

2.

Since CD is parallel to AB, the slopes of CD and AB are equal.

So, the slope of CD is −

3

2.

i) Point D is on the y-axis. So, it has coordinates (0, y).

Use the formula for the slope of a line:

Slope of CD =

−

3

2 =

−

3

2 =

(–6)(−3

2) = (–6)

9 =

18 =

The coordinates of point D are (0, 18). ii) Point D is on the x-axis. It has coordinates (x, 0).

Use the formula for the slope of a line:

Slope of CD =

−

3

2 =

−

3

2 =

(−3

2) =

=

(2) = (2)( )

= –18 –3x = –36

x = 12 The coordinates of point D are (12, 0).

PTS: 1 DIF: Difficult REF: 6.2 Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Problem-Solving Skills

85. ANS: a) The student may have interchanged the signs of the slope and y-intercept. b) Use the equation:

To write the equation of a linear function, determine the slope of the line, m, and its y-intercept, b. The line intersects the y-axis at 2; so, . From the graph, the rise is when the run is .

So, , or

Substitute for m and b in .

The equation of the graph is:

PTS: 1 DIF: Moderate REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

86. ANS: Substitute the coordinates of point J(–5, 2) into the equation , then solve for m.

So, when the line passes through the point J(–5, 2), the value of m is .

PTS: 1 DIF: Difficult REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Problem-Solving Skills

87. ANS: a) The flat fee is: $50

When n T-shirts are ordered, the additional cost is: 8.95n dollars So, an equation is:

b) Use the equation:

The total cost was $604.90. c) Use the equation:

Jakub ordered 103 T-shirts.

PTS: 1 DIF: Moderate REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Problem-Solving Skills

88. ANS: a) n = f(t), so two points on the graph have coordinates C(25, 458) and D(29, 534).

Use this form for the equation of a linear function:

Substitute: , , , and

In slope-point form, the equation that represents this function is: b) Use:

Substitute:

When the students sell 325 cups of punch, the approximate temperature is 18°C.

PTS: 1 DIF: Difficult REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Problem-Solving Skills

89. ANS: Since the coordinates of 2 points on the line are known, use this form for the equation of a linear function:

Substitute: , , , and

In general form, an equation that represents the line that passes through A(3, –4) and B(11, 8) is:

PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF7 | 10.RF5 TOP: Relations and Functions KEY: Problem-Solving Skills

90. ANS: Sample answer: Determine the x- and y-intercepts. To determine the x-intercept, substitute y = 0:

The x-intercept is 4 and is described by the point (4, 0). To determine the y-intercept, substitute x = 0:

The y-intercept is and is described by the point (0, ). On a grid, plot the points that represent the intercepts. Draw a line through the points.

0

x - 4y - 4 = 0

4 8 12 16–4–8–12–16 x

4

8

–4

–8

y

PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF7 | 10.RF5 TOP: Relations and Functions KEY: Communication | Problem-Solving Skills

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