Math 3 Unit 6: Radical Functions - cusd.com
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Math 3 Unit 6: Radical Functions
Unit Title Standards
6.1 Simplifying Radical Expressions N.RN.2, A.SSE.2
6.2 Multiplying and Dividing Radical Expressions N.RN.2, F.IF.8
6.3 Adding & Subtracting Radical Expressions N.RN.2, A.SSE.2
6.4 Multiplying & Dividing Binomial Radical Expressions N.RN.2, A.SSE.2
6.5 Rational Exponents N.RN.1, N.RN.2
6.6 Solving Radical Equations A.REI.2
6.7 Graphing Radical Equations F.IF.7B, F.IF.5
6.8 Graphing Radical Equations with Cubed Roots F.IF.7B, F.IF.5
6.9 Solving and Graphing Radical Equations A.REI.11
Unit 6 Review
Additional Clovis Unified Resources http://mathhelp.cusd.com/courses/math-3 Clovis Unified is dedicated to helping you be successful in Math 3. On the website above you will find videos from Clovis Unified teachers on lessons, homework, and reviews. Digital copies of the worksheets, as well as hyperlinks to the videos listed on the back are also available at this site.
Math 3 Unit 6: Online Resources 6.1 Simplifying
Radical Expressions
β’ Khan Academy: Simplifying Radical Terms http://bit.ly/61srea or http://bit.ly/61sreb
β’ Purple Math: Square Roots & More Simplification http://bit.ly/61srec or http://bit.ly/61sree
β’ Patrick JMT: Radical Notation and Simplifying Radicals (Basic) http://bit.ly/61sref
6.2 Multiplying and Dividing Radical Expressions
β’ Khan Academy: Rationalizing the Denominator http://bit.ly/62mdrea
β’ Khan Academy: Rational Expressions - Multiplying and Dividing http://bit.ly/62mdreb or http://bit.ly/62mdrec
β’ Purple Math: Rationalizing Denominators http://bit.ly/62mdred
6.3 Adding & Subtracting Radical Expressions
β’ Khan Academy: Adding Radical Expressions http://bit.ly/63asreb
β’ Khan Academy: Subtracting Radical Expressions http://bit.ly/63asrec
β’ Purple Math: Adding and Subtracting Radical Expressions http://bit.ly/63asred
6.4 Multiplying & Dividing Binomial Radical Expressions
β’ Open Algebra: Multiplying and Dividing Radical Expressions (multiple video links at the end) http://bit.ly/64mdba
β’ Multiplying Binomial Radical Expressions http://bit.ly/64mdbb
6.5 Rational Exponents
β’ Patrick JMT: Evaluating Numbers with Rational Exponents by using Radical Notation http://bit.ly/65raexa
β’ Patrick JMT: Multiplying Variables with Rational Exponents β Basic Ex 1 & Ex 2 http://bit.ly/65raexb or http://bit.ly/65raexc
β’ Khan Academy: Simplifying Rational Exponents http://bit.ly/65raexd
6.6 Solving Radical Equations
β’ Patrick JMT: Solving Equations Involving Rational Exponents http://bit.ly/66srea
β’ Patrick JMT: Solving Equations Involving Square Roots http://bit.ly/66sreb
β’ Khan Academy: Solving Square-Root Equations http://bit.ly/66srec
6.7 Graphing Radical Equations
β’ Khan Academy: Graphs of Square-Root Functions http://bit.ly/67grea
β’ Khan Academy: Square-Root Functions & their Graphs http://bit.ly/67greb
6.8 Graphing Radical Equations with Cubed Roots
β’ Math Bits Notebook: Square-Root & Cube Root Functions http://bit.ly/68grea
β’ Snap Math: Domain and Range of Cubed Root http://bit.ly/68greb
β’ Graphing Cube Root Functions http://bit.ly/68grec
6.9 Solving and Graphing Radical Equations
β’ Purple Math: Graphing Radical Functions (Pages 1-3) http://bit.ly/69sgrea
β’ Patrick JMT: Solving an Equation Involving a Single Radical (Square Root) β Ex 1 http://bit.ly/69sgreb
β’ Patrick JMT: Solving an Equation Containing Two Radicals β Ex 1 http://bit.ly/69sgrec
Math 3 Unit 6 Worksheet 1
Math 3 Unit 6 Worksheet 1 Name: Simplifying Radical Expressions Date: Per:
[1-6] Simplify.
1. β25 2. β0.09 3. οΏ½ 49121
4. β273 5. ββ 83 6. οΏ½ 64125
3
[7- 9] Find each real root.
7. β36 8. ββ273 9. β0.01
[10-29] Simplify each radical expression. Use absolute value symbols when needed.
10. β25π₯π₯2 11. βππ6ππ12 12. β9ππ4ππ2 13. οΏ½16π₯π₯2π¦π¦8
14. οΏ½121π₯π₯3π¦π¦12 15. β3π₯π₯οΏ½81π₯π₯7π¦π¦2 16. 2β24ππ4ππ9 17. ππβ27ππ5ππ6
18. 3π₯π₯2οΏ½40π₯π₯π¦π¦4 19. β75ππ8ππ7 20. β8π₯π₯33 21. οΏ½27π₯π₯12π¦π¦153
Math 3 Unit 6 Worksheet 1
22. οΏ½β64π₯π₯3π¦π¦63 23. οΏ½π₯π₯14π¦π¦53 24. ββππππ3ππ43 25. 2π₯π₯οΏ½β24π₯π₯3π¦π¦53
26. οΏ½32π₯π₯9π¦π¦103 27. οΏ½16π₯π₯4π¦π¦93 28. 3π₯π₯2 ββ40π₯π₯83 29. ββ54ππ6ππ11ππ73
[30-34] Find all the real solutions of each equation.
30. π₯π₯2 = 36 31. π₯π₯3 = 8 32. π₯π₯2 = 0.81 33. π₯π₯3 = β27 34. π₯π₯2 = 16
35. Determine whether each expression is equivalent to οΏ½32π₯π₯3π¦π¦2. Select Yes or No for each expression.
36. Determine whether each expression is equivalent to οΏ½64π₯π₯6π¦π¦53 . Select Yes or No for each expression.
Yes No 2π₯π₯οΏ½8π₯π₯π¦π¦2
4π₯π₯π¦π¦β2π₯π₯
4π₯π₯|π¦π¦|β2π₯π₯
16π₯π₯οΏ½π₯π₯π¦π¦2
Yes No 2|π₯π₯| οΏ½8π₯π₯π¦π¦53
4π₯π₯ οΏ½π₯π₯π¦π¦53
4π₯π₯2π¦π¦2 οΏ½π¦π¦33
(2π₯π₯)2π¦π¦ οΏ½π¦π¦23
Math 3 Unit 6 Worksheet 2
Math 3 Unit 6 Worksheet 2 Name: Multiplying & Dividing Radical Expressions Date: Per: [1-4] Simplify each expression.
1. β128π₯π₯53 2. β81π₯π₯73 3. οΏ½64π₯π₯6π¦π¦74 4. β32π₯π₯54
[5-19] Multiply and simplify, if possible, assuming all variable expressions are real numbers. 5. β43 β β163 6. β5 β β50 7. β93 β β93 8. β3 β ββ4 9. ββ123 β ββ183 10. β23 β β7 11. β8π₯π₯βοΏ½6π₯π₯π¦π¦2 12. 3οΏ½16π₯π₯4π¦π¦3 β 2οΏ½π₯π₯π¦π¦23 13. π₯π₯ οΏ½27π₯π₯2π¦π¦3 β 2π₯π₯ βπ₯π₯33 14. 5β2ππππ6 β β2ππ3ππ 15. βππ5ππ5 β 3β2ππ7ππ6 16. β18ππ94 β β9ππππ44 17. βοΏ½2π₯π₯3π¦π¦23 β 4οΏ½12π₯π₯5π¦π¦3 18. β2(β50 + 7) 19. β6(β6 + β18) 20. For the multiplication οΏ½2π₯π₯π¦π¦ β οΏ½3π₯π₯3π¦π¦5, where x and y are real numbers, state the possible positive/negative configurations of the variables and explain the reasoning.
Math 3 Unit 6 Worksheet 2
[21-30] Simplify each expression. Rationalize all denominators. Assume all variables represent positive numbers.
21. β5β10
22. 1β53 23.
2β63 24.
1β84
25. 7β34β6ππ
26. 1
β16ππ3 27. 8β25π₯π₯23
28. β6π₯π₯4
οΏ½5π₯π₯2π¦π¦5 29.
2οΏ½7π₯π₯3π¦π¦β3οΏ½12π₯π₯4π¦π¦
30. β123
οΏ½6π₯π₯2π¦π¦3
31. Determine whether each expression is equivalent to β81π₯π₯73 . Select Yes or No for each expression.
Yes No 3οΏ½3π₯π₯73
9οΏ½π₯π₯73
3π₯π₯2 β3π₯π₯3
3π₯π₯ οΏ½3π₯π₯43
32. Determine whether each expression is equivalent to β20π₯π₯ β οΏ½10π₯π₯3π¦π¦5. Select Yes or No for each expression.
Yes No 2β5π₯π₯ β π¦π¦οΏ½10π₯π₯3π¦π¦3
|π₯π₯2|οΏ½200π¦π¦5
2π¦π¦2οΏ½10π₯π₯4
10(π₯π₯π¦π¦)2οΏ½2π¦π¦
Math 3 Unit 6 Worksheet 3
Math 3 Unit 6 Worksheet 3 Name: Adding & Subtracting Radical Expressions Date: Per: Simplify, if possible. Assume all variables represent positive real numbers.
1. 10β5 + 2β5 2. 9β2 + 5β23 3. 5β11π₯π₯ β 8β11π₯π₯
4. 4β5 + 5β7 5. 9βπ₯π₯23 β 4βπ₯π₯23 6. 3β543 β 8β543
7. 5β3 + β12 8. 11β50 + β8 9. β163 + β543
10. 5β813 β 3β543 11. β72 + β18 + β50 12. β75 + 6β27 β 2β3
13. 4β18 + 6β75 β 2β48 14. β163 + 5β1283 β 2β543 15. 7β8π₯π₯ β 2β98π₯π₯
16. 4β9π₯π₯ β 2βπ₯π₯ 17. 4β216π€π€2 + 3β54π€π€2 18. β12π₯π₯33 + 4β27π₯π₯3
Math 3 Unit 6 Worksheet 3
19. β25π₯π₯5 + 3π₯π₯2β49π₯π₯ 20. π₯π₯β40π₯π₯43 β β135π₯π₯73 21. π₯π₯β343π₯π₯3 + β729π₯π₯43
22. οΏ½4 β β6οΏ½οΏ½4 + β6οΏ½ 23. οΏ½3β7 + 5οΏ½οΏ½3β7 β 5οΏ½ 24. οΏ½β3 + β10οΏ½οΏ½β3 β β10οΏ½ 25. Determine whether each expression is equivalent to β50 + β8. Select Yes or No for each expression.
Yes No β58
5β2 + 2β2 9
(4 + 3)β2
26. Determine whether each expression is equivalent to 5β16π₯π₯ β 3βπ₯π₯. Select Yes or No for each expression.
Yes No 20βπ₯π₯ β 3βπ₯π₯
17 2β15π₯π₯
17βπ₯π₯
Math 3 Unit 6 Worksheet 4
Math 3 Unit 6 Worksheet 4 Name: Multiplying & Dividing Binomial Radical Expressions Date: Per: Simplify, if possible. Assume all variables represent positive real numbers.
1. οΏ½3 β 6β2οΏ½οΏ½5 β 4β2οΏ½ 2. οΏ½3 + β5οΏ½οΏ½3 β β5οΏ½ 3. οΏ½2 β β5οΏ½2
4. οΏ½2 + 5β7οΏ½οΏ½5 + 4β7οΏ½ 5. οΏ½5 + 4β3οΏ½οΏ½1 β 2β3οΏ½ 6. οΏ½9β5 + 7οΏ½οΏ½9β5 β 7οΏ½
7. οΏ½β3 + β7οΏ½2 8. οΏ½2 β 4β3οΏ½οΏ½2 + 4β3οΏ½ 9. οΏ½1 + β98οΏ½οΏ½5 + β2οΏ½
10. οΏ½3 + 2β3οΏ½2 11. οΏ½β7 β β3οΏ½οΏ½β7 + β3οΏ½ 12. οΏ½βπ₯π₯ β β5οΏ½οΏ½βπ₯π₯ β 6β5οΏ½
13. οΏ½β12 + β50οΏ½2 14. οΏ½β1.25β β1.8οΏ½οΏ½β5 β β0.2οΏ½ 15. οΏ½βπ₯π₯ + 2 β βπ₯π₯ β 2οΏ½οΏ½βπ₯π₯ + 2 + βπ₯π₯ β 2οΏ½
Math 3 Unit 6 Worksheet 4
16. 5
1+β2 17.
9β5β3
18. β3
8+β7
19. 6
4ββ10 20.
12β23β9
21. β49
β9+β16
22. 2+β83β8β2
23. 2+3β279ββ27
24. Find the perimeter and area of the rectangle 25. Find the unknown side and verify the area
4β5 β 7
2β5 + 4
???
β13 + 3
π΄π΄π΄π΄π΄π΄π΄π΄ = 16
Math 3 Unit 6 Worksheet 5
Math 3 Unit 6 Worksheet 5 Name: Rational Exponents Date: Per: [1-14] Simplify each expression. 1. 81
12 2. 125
23 3. 16β
14 4. 9β
32 5. 3
12 β 3
12
6. (β8)13 β (β8)
13 7. (β32)0.8 8. 2431.25 9. 100β1.5 10. 16
12
1614
11. 100023
10012
12. 6413
813
13. οΏ½27β23οΏ½β1
14. (2532)
13
[15-19] Write each expression in radical form. 15. π₯π₯
12 16. π₯π₯
23 17. π¦π¦1.25 18. π¦π¦β
23 19. π¦π¦β
34
[20- 24] Write each expression in exponential form. 20. β6 21. βοΏ½π¦π¦23 22. οΏ½οΏ½π¦π¦4 οΏ½
3 23. οΏ½οΏ½2π₯π₯π¦π¦3 οΏ½
6 24. β7π₯π₯
Math 3 Unit 6 Worksheet 5
[25-39] Write each expression in simplest form. Assume all variables represent positive real numbers.
25. (27π₯π₯9)13 26. (81π₯π₯12)β
14 27. οΏ½125π₯π₯6 π¦π¦
12οΏ½
23
28. οΏ½32π₯π₯10 π¦π¦12οΏ½
25 29. οΏ½8π₯π₯
34π¦π¦6οΏ½
43 30. π₯π₯
23 β π₯π₯
13
31. π¦π¦
12 β 2π¦π¦
14 32. 4π₯π₯
25 β 3π₯π₯
310 33. π₯π₯
34 Γ· π₯π₯
18
34. π₯π₯12 π¦π¦β
12
π₯π₯14 π¦π¦β
32 35. οΏ½ π₯π₯
12
π¦π¦β34οΏ½8
36. οΏ½27π₯π₯9
8π¦π¦12οΏ½13
37. οΏ½18π₯π₯12
2π¦π¦4οΏ½12 38. οΏ½ 2π₯π₯6
128π¦π¦15οΏ½23 39. οΏ½27π₯π₯
4
48π¦π¦2οΏ½32
Math 3 Unit 6 Worksheet 6
Math 3 Unit 6 Worksheet 6 Name: Solving Radical Equations Date: Per: [1-8] Solve the following for x. 1. 4βπ₯π₯ + 3 = 15 2. β2π₯π₯ + 3 β 5 = 0 3. 5π₯π₯
23 = 45
4. πποΏ½ππ(π₯π₯)οΏ½ = 16 5. πποΏ½ππ(π₯π₯)οΏ½ = 27 6. πποΏ½ππ(π₯π₯)οΏ½ = 2
If ππ(π₯π₯) = 2π₯π₯34 and ππ(π₯π₯) = π₯π₯ β 2 If ππ(π₯π₯) = π₯π₯
32 and ππ(π₯π₯) = π₯π₯ β 1 If ππ(π₯π₯) = π₯π₯
13 and ππ(π₯π₯) = π₯π₯ + 1
7. (π₯π₯ + 4)34 β 6 = 21 8. 2π₯π₯
12 + 4 = 6
[9-20] Solve the following for x. Check for extraneous solutions. 9. βπ₯π₯ + 3 = π₯π₯ + 1 10. β2π₯π₯ = βπ₯π₯ + 5 11. π₯π₯ β 6 = β3π₯π₯
Math 3 Unit 6 Worksheet 6
12. ππ(π₯π₯) β ππ(π₯π₯) = 0 13. β5 β 4π₯π₯ = β3 14. β4 β 11π₯π₯ = βπ₯π₯ + 2 If ππ(π₯π₯) = β5 β 4π₯π₯ and ππ(π₯π₯) = π₯π₯
15. ππ(π₯π₯) β ππ(π₯π₯) = 0 16. βπ₯π₯ + 2 + 4 = π₯π₯ 17. βπ₯π₯2 + 3 = π₯π₯ + 1 If ππ(π₯π₯) = β1 β π₯π₯ and ππ(π₯π₯) = π₯π₯ + 1
18. βπ₯π₯ β βπ₯π₯ β 5 = 2 19. βπ₯π₯ + 9 = 1 + β2 + π₯π₯ 20. βπ₯π₯ = βπ₯π₯ β 8 + 2
Math 3 Unit 6 Worksheet 7
Math 3 Unit 6 Worksheet 7 Name: Graphing Radical Equations Date: Per: [1-6] Graph each function and state the domain and range.
1. π¦π¦ = βπ₯π₯ + 5 2. π¦π¦ = βπ₯π₯ + 3 3. π¦π¦ = ββπ₯π₯ β 2 Domain Domain Domain
Range Range Range 4. π¦π¦ = 3βπ₯π₯ + 1 β 6 5. π¦π¦ = β2βπ₯π₯ β 2 + 1 6. π¦π¦ = 1
2 βπ₯π₯ + 2 + 3 Domain Domain Domain
Range Range Range [7-11]: Sketch the graph for each of the following and find/solve for the indicated information.
7. ππ(π₯π₯) = βπ₯π₯ + 4 a) Domain & Range
b) π₯π₯ β ππππππ π¦π¦ β ππππππππππππππππππ(π π )
c) The open interval where ππ is increasing d) The average rate of change for ππ on 0 β€ π₯π₯ β€ 9
Math 3 Unit 6 Worksheet 7
8. ππ(π₯π₯) = 5 β βπ₯π₯ a) Domain & Range b) π₯π₯ β ππππππ π¦π¦ β ππππππππππππππππππ(π π ) c) The open interval where ππ is decreasing d) The open interval where ππ is negative 9. β(π₯π₯) = βπ₯π₯ + 2 β 3 a) Domain & Range b) π₯π₯ β ππππππ π¦π¦ β ππππππππππππππππππ(π π ) c) The open interval where β is positive d) The average rate of change for β on β1 β€ π₯π₯ β€ 7 10. π¦π¦ = 1
2 βπ₯π₯ + 1 β 2 a) Domain & Range b) π₯π₯ β ππππππ π¦π¦ β ππππππππππππππππππ(π π ) c) The open interval where the function is increasing d) The average rate of change for this function from π₯π₯ = 3 to π₯π₯ = 15 11. ππ(π₯π₯) = 3 β 2βπ₯π₯ + 4 a) Domain & Range b) π₯π₯ β ππππππ π¦π¦ β ππππππππππππππππππ(π π ) c) The average rate of change for ππ from π₯π₯ = β3 to π₯π₯ = 5 d) The open interval where ππ is positive
Math 3 Unit 6 Worksheet 8
Math 3 Unit 6 Worksheet 8 Name: Graphing Radical Equations Date: Per: [1-6] Graph each function and state the domain and range.
1. π¦π¦ = βπ₯π₯3 + 2 2. π¦π¦ = βπ₯π₯ β 33 3. π¦π¦ = ββπ₯π₯3 β 1 Domain Domain Domain
Range Range Range 4. π¦π¦ = 2βπ₯π₯ + 13 β 4 5. π¦π¦ = β2βπ₯π₯ β 23 + 1 6. π¦π¦ = 1
2 βπ₯π₯ + 23 + 3 Domain Domain Domain
Range Range Range
Math 3 Unit 6 Worksheet 8
[7-8]: Sketch the graph for each of the following and find/solve for the indicated information.
7. ππ(π₯π₯) = 1 β βπ₯π₯ + 23 a) Domain & Range
b) π₯π₯ β ππππππ π¦π¦ β ππππππππππππππππππ(π π )
c) The open interval where ππ is decreasing
d) The open interval where ππ is negative
8. β(π₯π₯) = 2βπ₯π₯ β 33 + 2 a) Domain & Range
b) π₯π₯ β ππππππ π¦π¦ β ππππππππππππππππππ(π π )
c) The open interval where β is negative
d) The average rate of change for β on β5 β€ π₯π₯ β€ 2
Math 3 Unit 6 Worksheet 9
Math 3 Unit 6 Worksheet 9 Name: Solving and Graphing Radical Equations Date: Per:
1. a) Solve algebraically for π₯π₯: βπ₯π₯ + 1 = π₯π₯ β 1 b) Accurately graph the system of equations which is from the algebraic equation in part a) .
ππ(π₯π₯) = βπ₯π₯ + 1 and ππ(π₯π₯) = π₯π₯ β 1
ππ(π₯π₯) = ππ(π₯π₯) ππππ π₯π₯ = ____
2. a) Solve algebraically for π₯π₯: ββπ₯π₯ + 7 = βπ₯π₯ β 1 b) Rewrite the algebraic equation into a system of
equations and accurately graph.
ππ(π₯π₯) = ππ(π₯π₯) ππππ π₯π₯ = ____
3. a) Solve algebraically for π₯π₯: βπ₯π₯ + 3 = 2π₯π₯ b) Rewrite the algebraic equation into a system of
equations and accurately graph.
ππ(π₯π₯) = ππ(π₯π₯) ππππ π₯π₯ = ____
4. a) Solve algebraically for π₯π₯: ββπ₯π₯ β 4 = π₯π₯ β 10 b) Rewrite the algebraic equation into a system of
equations and accurately graph.
ππ(π₯π₯) = ππ(π₯π₯) ππππ π₯π₯ = ____
Math 3 Unit 6 Worksheet 9
[5-19] Solve the following for x. Check for extraneous solutions. 5. 1
3βπ₯π₯ + 5 β 2 = 2 6. 17β 3βπ₯π₯ β 4 = 2 7. πποΏ½ππ(π₯π₯)οΏ½ = 15 If ππ(π₯π₯) = βπ₯π₯ and ππ(π₯π₯) = π₯π₯ + 2 8. 4βπ₯π₯ + 33 + 17 = 9 9. 2ππ(π₯π₯) + 19 = 3 10. β8π₯π₯ + 9 = 3βπ₯π₯ If ππ(π₯π₯) = βπ₯π₯ + 1 11. β10π₯π₯ + 8 = 2β3π₯π₯ 12. 3β5π₯π₯ + 3 = 6β2π₯π₯ 13. 2βπ₯π₯ = β3π₯π₯ + 6 14. ππ(ππ(π₯π₯)) = ππ(π₯π₯) β 2 15. βπ₯π₯ β 2 = 4 β π₯π₯ 16. β2π₯π₯ + 5 = π₯π₯ + 1 If ππ(π₯π₯) = π₯π₯ + 2 and ππ(π₯π₯) = βπ₯π₯ 17. 3π₯π₯ β 5βπ₯π₯ = 2 18. β2π₯π₯ + 5 = 2β2π₯π₯ + 1 19. βπ₯π₯ + 7 = π₯π₯ β 5
Math 3 Unit 6 Review Worksheet 1
Math 3 Unit 6 Review Worksheet 1 Name: Radical Functions Date: Per: [1-18] Simplify the following:
1. β49ππ2 2. β27ππ4 3. β121ππ6ππ8 4. ββ273 5. β8ππ33 6. ββ325 7. β80ππ4ππ5 8. β147ππ3ππ4
9. 18β13+2
10. 1β43 11. 5
οΏ½25π₯π₯23 12. οΏ½20π₯π₯4π¦π¦2
οΏ½5π₯π₯π¦π¦3
13. 3π₯π₯β7π₯π₯
14. β8π₯π₯3 + 3π₯π₯β2π₯π₯ 15. 4ππβ75ππππ6 β 2ππ2β48ππ3ππ2
16. 7οΏ½2π₯π₯3π¦π¦6 β οΏ½2π₯π₯π¦π¦ 17. οΏ½27π₯π₯2π¦π¦ β οΏ½π₯π₯3π¦π¦5 18. β3
β7 β 5
Math 3 Unit 6 Review Worksheet 1
19. Rewrite the functions below so they are translated 5 units left and 7 units up. Sketch the translated function. a) π¦π¦ = π₯π₯2 b) π¦π¦ = (π₯π₯ β 2)2 + 3 c) π¦π¦ = |π₯π₯| d) π¦π¦ = |π₯π₯ + 2| + 1 e) π¦π¦ = βπ₯π₯ f) π¦π¦ = βπ₯π₯ + 1 β 2 g) π¦π¦ = βπ₯π₯3 h) π¦π¦ = βπ₯π₯ β 13 β 1
20. Given: ππ(π₯π₯) = (π₯π₯ β 2)2 + 5 , π₯π₯ β₯ 2 . Sketch ππ(π₯π₯) and identify its domain and range.
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Math 3 Unit 6 Review Worksheet 1
21. Given: ππ(π₯π₯) = βπ₯π₯ and ππ(π₯π₯) = π₯π₯ β 3
Sketch π¦π¦ = βππ(ππ(π₯π₯)) and identify its domain and range.
[22-24] Solve the following equation for x: 22. 1
4 βπ₯π₯ + 3 β 1 = 0 23. β2π₯π₯ + 10 = β4π₯π₯ 24. β2π₯π₯2 + 16 = 2β3π₯π₯ 25. a) Solve the following equation algebraically for π₯π₯: βπ₯π₯ β 2 = π₯π₯ β 4 b) Rewrite the above equation as a system of two equations and graph. ππ(π₯π₯) = ππ(π₯π₯) = For ππ(π₯π₯) = ππ(π₯π₯), π₯π₯ =
Math 3 Unit 6 Review Worksheet 1
[26-28] Graph the following and find the following: a) x-intercept and y-intercept b) Domain and Range c) the open interval where f is increasing d) the open interval where f is decreasing e) the open interval where f is negative f) the open interval where f is positive g) Average rate of change on the specified interval
β’ [3, 7] for problem #6 β’ [β2, 1] for problem #7 β’ [β4, 4] for problem #8
26. ππ(π₯π₯) = 12 βπ₯π₯ β 3 β 1
27. ππ(π₯π₯) = 4 β βπ₯π₯ + 3 28. ππ(π₯π₯) = 1
2 βπ₯π₯ + 43 β 1
Math 3 Unit 6 Review Worksheet 1
29. Determine whether each expression is equivalent to οΏ½32π₯π₯3π¦π¦2. Select Yes or No for each expression.
30. Selected Response: Given ππ(π₯π₯) = π₯π₯2 β 4 and ππ(π₯π₯) = π₯π₯ + 2, which of the following is true? Choose ALL that apply.
(A) ππ(π₯π₯)ππ(π₯π₯)
= π₯π₯ β 2, π₯π₯ β β2 (B) πποΏ½ππ(π₯π₯)οΏ½ = π₯π₯2 + 4π₯π₯ (C) (ππ β ππ)(π₯π₯) = π₯π₯2 β 2
[31-35]: Matching. 31. π¦π¦ = βπ₯π₯ β 2 β 1 32. π¦π¦ = ββπ₯π₯ β 2 β 1 33. π¦π¦ = βπ₯π₯ β 23 β 1 34. π¦π¦ = ββπ₯π₯ + 2 β 1
35. π¦π¦ = ββπ₯π₯ + 23 β 1
Yes No 4π₯π₯οΏ½2π₯π₯π¦π¦2
22π₯π₯π¦π¦β2π₯π₯
4π₯π₯|π¦π¦|β2π₯π₯
2π₯π₯οΏ½2π₯π₯π¦π¦2
2π₯π₯|π¦π¦|β8π₯π₯
A)
C) D)
E)
H)
F)
B)
G)
Math 3 Unit 6 Review Worksheet 1
[36-38]: Solve for x. 36. 75 β 4βπ₯π₯ β 5 = 39 37. 3β5π₯π₯ + 4 = 6β2π₯π₯ 38. βπ₯π₯ + 3 = βπ₯π₯ β 1 39. Go back to problem #38. Rewrite the equation as a system of two equations and graph both on the coordinate axes to the right. Find the solution(s) to the system based on the graph. 40. Given ππ(π₯π₯) = 2βπ₯π₯ + 5 β 4 a) Sketch. b) Identify domain & range. c) Find x-int & y-int. d) Identify open interval where f is increasing. e) Identify open interval where f is decreasing. f) Identify open interval where f is positive. g) Identify open interval where f is negative. h) Find the average rate of change for f on β4 β€ π₯π₯ β€ 11. 41. If ππ(π₯π₯) = ββπ₯π₯ β 2 β 7, find its domain & range.
Math 3 Unit 6 Review Worksheet 2
Math 3 Unit 6 Review Worksheet 2 Name: Radical Functions Date: Per: [1-6] Selected Response: Choose all answers that apply 1. Choose which of the following expression(s) is equivalent to οΏ½81π₯π₯3π¦π¦2 1. {Hint: There are two correct responses} A) 3π₯π₯|π¦π¦|βπ₯π₯ B) 32π₯π₯οΏ½π₯π₯π¦π¦2 C) 9π¦π¦βπ₯π₯3 D) 9π₯π₯|π¦π¦|βπ₯π₯ E) 9π₯π₯π¦π¦βπ₯π₯
2. Choose which of the following expression(s) is equivalent to β16 2. {Hint: There are three correct responses} A) β 8 B) 8 C) (β2)2 D) 22 E) 4 3. Choose which of the following expression(s) is equivalent to 4 12x x 3. {Hint: There are three correct responses} A) 8π₯π₯β3π₯π₯ B) 24βπ₯π₯3 C) 6π₯π₯β3π₯π₯ + 2π₯π₯β3π₯π₯ D) 8β3π₯π₯3 E) 12π₯π₯β2π₯π₯
4. Choose which of the following expression(s) is equivalent to οΏ½β8π₯π₯3π¦π¦63 4. {Hint: There are two correct responses} A) 2|π₯π₯|π¦π¦2 B) β2|π₯π₯|π¦π¦2 C) 2π₯π₯π¦π¦3 D) β2π₯π₯π¦π¦2 E) β4
2π₯π₯π¦π¦3
5. Choose which of the following expression(s) is equivalent to β8π₯π₯ + β2π₯π₯ 5. {Sorry, no hints this time.} A) 3β2π₯π₯ B) 2β2π₯π₯ + β2π₯π₯ C) β10π₯π₯ D) β10π₯π₯2 E) |π₯π₯|β10
6. Choose which of the following expression(s) is equivalent to (4 β β2)(2 + β2) 6. {Sorry, no hints this time.} A) 8 + 4β2 β 2β2 β 2 B) 6 C) 8 + β8 β β4 β β4 D) 2(3 + β2) E) 6 + 2β2
Math 3 Unit 6 Review Worksheet 2
7. Graph: ππ(π₯π₯) = ββπ₯π₯ + 5 + 3 A. Sketch the graph
B. Domain: Range
C. Identify the x-intercept: show work
D. Identify the y-intercept:
E. Open interval where ππ is increasing
F. Open interval where ππ is positive
G. Identify the rate of change over β4 β€ π₯π₯ β€ 44 show work
H. Rewrite ππ if it were shifted 7 units to the left and 2 units down ππ(π₯π₯) =
Original Vertex:
Shift:
New Vertex:
8. Rationalize: 207β3
9. Rationalize: 3
7ββ2 8.
9.
10. Simplify: 2β10ππππ β 6β14ππππ2 11. Rationalize: 8 β7 3
2 β253 10.
11.
Math 3 Unit 6 Review Worksheet 2
12. Simplify: 5ππβ80ππ33 + 3ππ2β103 12.
13. Simplify: 3ππ5 οΏ½8π₯π₯7
πποΏ½6π₯π₯8 13.
14. Cube root graphing: A. Graph ππ(π₯π₯) = β βπ₯π₯ + 33 β 5
B. Domain Range
C. This function is: always increasing / always decreasing / at times increasing and at times decreasing
(Circle the correct answer)
D. Identify the x-intercept: show work
E. Identify the y-intercept:
F. Open interval where ππ is positive G. Open interval where ππ is negative
15. Multiply: (2 + 3β5)(5 β 2β5) 16. Simplify: οΏ½8 β 3β2οΏ½2
15. 16.
Math 3 Unit 6 Selected Answers
Selected Answers to Math 3 Unit 6 Worksheet #7:
7 ππ) π·π·: π₯π₯ β₯ 0 ππππ [0,β);π π : π¦π¦ β₯ 4 ππππ [4,β) ππ) (0, 4) ππ) π₯π₯ β₯ 0 ππππ (0,β) ππ) 1/3
9 ππ) π·π·: π₯π₯ β₯ β2 ππππ [β2,β);π π :π¦π¦ β₯ β3 ππππ [β3,β) ππ) (7, 0) ππππππ (0,β2 β 3) β (0,β1.586) ππ) π₯π₯ > 7 ππππ (7,β) ππ) 1/4
11 ππ) π·π·:π₯π₯ β₯ β4 ππππ [β4,β);π π : π¦π¦ β€ β3 ππππ (ββ,β3] ππ) (β7/4, 0) ππππππ (0,β1) ππ) β 1/2 ππ) β 4 < π₯π₯ < β7/4 ππππ (β4,β7/4)
Selected Answers to Math 3 Unit 6 Worksheet #1: 1. Β±5 3. Β± 7
11 5. β 2 7. 6 9. 0.1 11. |ππ3|ππ6 13. 4|π₯π₯|π¦π¦4 15. β27π₯π₯4|π¦π¦|βπ₯π₯ 17. 3ππ3|ππ3|β3ππ
19. 5ππ4ππ3β3ππ 21. 3π₯π₯4π¦π¦5 23. π₯π₯4π¦π¦ οΏ½π₯π₯2π¦π¦23 25. β4π₯π₯2π¦π¦ οΏ½3π¦π¦23 27. 2π₯π₯π¦π¦3 β2π₯π₯3 29. β3ππ2ππ3ππ2 ββ2ππ2ππ3 31. π₯π₯ = 2 33. π₯π₯ = β3 Selected Answers to Math 3 Unit 6 Worksheet #2: 1. 4π₯π₯β2π₯π₯23 3. 2|π₯π₯|π¦π¦ οΏ½4π₯π₯2π¦π¦34 5. 4 7. 3β33 9. 6 11. 4π₯π₯|π¦π¦|β3 13. 6π₯π₯3 οΏ½3π₯π₯2π¦π¦3 15. π₯π₯2π¦π¦3β6
17. 3ππ2|ππ|β2ππ24 19. 10 + 7β2 21. β22
23. β363
3 25. 7β2ππ
8ππ 27. 8 β5π₯π₯
3
5π₯π₯ 29. ββ21π₯π₯
9π₯π₯
Selected Answers to Math 3 Unit 6 Worksheet #3: 1. 12β5 3. β3β11π₯π₯ 5. 5βπ₯π₯23 7. 7β3 9. 5β23 11. 14β2 13. 12β2 + 22β3 15. 0 17. 33π€π€β6 19. 26π₯π₯2βπ₯π₯ 21. 16π₯π₯ βπ₯π₯3 23. 38 Selected Answers to Math 3 Unit 6 Worksheet #4: 1. 63β 42β2 3. 9 β 4β5 5. β19 β 6β3 7. 10 + 2β21 9. 19 + 36β2 11. 4 13. 62 + 20β6 15. 4
17. 9β5+27β4
19. 4 + β10 21. 1 23. 33+29β318
25. ? ? ? = 4β13 β 12 Selected Answers to Math 3 Unit 6 Worksheet #5: 1. 9 3. Β½ 5. 3 7. 16 9. 1
1000 11. 10 13. 9 15. βπ₯π₯ 17. οΏ½π¦π¦54 19. 1
οΏ½π¦π¦34 21. βπ¦π¦23 23. (2π₯π₯π¦π¦)2 25. 3π₯π₯3 27.
25π₯π₯4π¦π¦13 29. 16π₯π₯π¦π¦8 31. 2π¦π¦
34 33. π₯π₯
58 35. π₯π₯4π¦π¦6 37. 3π₯π₯
6
π¦π¦2 39. 27π₯π₯
6
64π¦π¦3
Selected Answers to Math 3 Unit 6 Worksheet #6: 1. π₯π₯ = 9 3. π₯π₯ = Β±27 5. π₯π₯ = 10 7. π₯π₯ = 77 9. π₯π₯ = 1 11. π₯π₯ = 12 13. β 15. π₯π₯ = 0 17. π₯π₯ = 1 19. π₯π₯ = 7
Selected Answers to Math 3 Unit 6 Worksheet #9: 1. {3}; 0 ππππ ππππ πππ₯π₯ππππππππππππππππ ππππππππ 3. {1};β3
4 ππππ ππππ πππ₯π₯ππππππππππππππππ ππππππππ 5. {139} 7. {223} 9. β 11. {4} 13. {6} 15.
{3 πππππππ¦π¦} 17. {4 πππππππ¦π¦} 19. {9 πππππππ¦π¦} Selected Answers to Math 3 Unit 6 Worksheet #10: 1. π₯π₯2 + 4π₯π₯ β 12; β 3. βπ₯π₯2 β 2π₯π₯ + 8; β 5. π₯π₯ + 3βπ₯π₯ β 10; [0,β) 7. 1
5 9. 1 11. βπ₯π₯2 + 2π₯π₯ β 4
13. β(2π₯π₯ β 4)2 15. (2π₯π₯ + 2)2 17. (ππ + 1)2
Selected Answers to Math 3 Unit 6 Worksheet #8:
7 ππ) π·π· & π π : ππππππ ππππππππππ ππππ (ββ,β) ππ) (β1,0); (0, 1 β β23 ) β (0,β0.260) ππ) ππππππ ππππππππππ ππππ (ββ,β) ππ) π₯π₯ > β1 ππππ (β1,β)
8 ππ) π·π· & π π : ππππππ ππππππππππ ππππ (ββ,β) ππ) (2, 0) ππππππ (0, 2 β 2β33 ) β (0,β0.884) ππ) π₯π₯ < 2 ππππ (ββ, 2) ππ) 27
Math 3 Unit 6 Selected Answers
Selected Answers to Math 3 Unit 6 Worksheet #11:
7. a) π¦π¦ = Β±οΏ½12
(π₯π₯ β 2) b) π·π·: β; π π : [2,β) c) π·π·: [2,β); π π : β d) Inverse is not a function
9. a) π¦π¦ = Β±ββπ₯π₯ + 2 b) π·π·: (ββ,β); π π : (ββ, 0] c) π·π·: (ββ, 0]; π π : (ββ,β) d) Inverse is not a function 11. a) π¦π¦ = 1π₯π₯
b) π·π·: π₯π₯ β 0; π π :π¦π¦ β 0 c) π·π·: π₯π₯ β 0; π π :π¦π¦ β 0 d) Inverse is a function 13. a) π¦π¦ = β 1π₯π₯
+ 3 b) 52 c) 1 d) x
Selected Answers to Math 3 Unit 6 Review WS 2: 1. BD 2. CDE 3. ACD 4. DE 5. AB 6. ADE 7. {86} 8. {4/3} 9. {β2}; 1 is extraneous 11. π₯π₯2 β π₯π₯ β 6 12. 1
2π₯π₯+1 , π₯π₯ β 3 13. 2π₯π₯2 + 3π₯π₯ β 5
14. b. π·π· = [β5,β) & π π = [β4,β) c. π₯π₯ β ππππππ = (β1,0) & π¦π¦ β ππππππ = (0,2β5β 4) d. (β5,β) e. β f. (β1,β) g. (β5,β1)
h. π΄π΄π΄π΄π΄π΄ ππππππππ ππππ ππβπππππ΄π΄ππ ππππ [β4, 11] = 2/5
15. a. ππ(π₯π₯): π·π· = [2,β) & π π = (ββ,β7]
b. ππβ1(π₯π₯): π·π· = (ββ,β7] & π π = [2,β) c. ππβ1(π₯π₯) = (π₯π₯ + 7)2 + 2; π₯π₯ β€ β7
Selected Answers to Math 3 Unit 6 Review WS 1: 25. {86} 26. {4/3} 27. {β2}; 1 is extraneous 29. π₯π₯2 β π₯π₯ β 6 30. 1
2π₯π₯+1 , π₯π₯ β 3 31. 2π₯π₯2 + 3π₯π₯ β 5 32. b. π·π· =
[β5,β) & π π = [β4,β) c. π₯π₯ β ππππππ = (β1,0) & π¦π¦ β ππππππ = (0,2β5 β 4) d. (β5,β) e. β f. (β1,β) g. (β5,β1) h. π΄π΄π΄π΄π΄π΄ ππππππππ ππππ ππβπππππ΄π΄ππ ππππ [β4, 11] = 2/5 33. a. ππ(π₯π₯): π·π· = [2,β) & π π = (ββ,β7] b. ππβ1(π₯π₯): π·π· = (ββ,β7] & π π = [2,β) c. ππβ1(π₯π₯) = (π₯π₯ + 7)2 + 2; π₯π₯ β€ β7