Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra 2 - Chapter 8 Review

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it.

____ 1. x –9 –7 –2 –1

y 36 28 8 4

a. inverse variation; y 324x

b. direct variation; y 4xc. neither

____ 2. Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse variation.

a. y 2x c. y 80

x

b. y 18x d. y = 0.8x

____ 3. Suppose that x and y vary inversely and that y 83 when x = 8. Write a function that models the inverse

variation and find y when x = 4.

a. y 13x ; 1

24 c. y 83x ; 8

3

b. y 83x ; 16

3 d. y 643x ; 16

3

____ 4. Suppose that y varies jointly with w and x and inversely with z and y = 175 when w = 5, x = 20 and z = 4. Write the equation that models the relationship. Then find y when w = 2, x = 24 and z = 6.

a. y 4wxz ; 32 c. y 7z

wx ; 78

b. y 4zwx ; 2 d. y 7wx

z ; 56

____ 5. The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 34 barrels of oil in traveling 60 miles at 20 mi/h. How many barrels of oil are used when the ship travels 32 miles at 23 mi/h? Round your answer to the nearest tenth of a barrel, if necessary.a. 3.0 barrels c. 18.1 barrelsb. 45.0 barrels d. 24.0 barrels

Name: ________________________ ID: A

2

Graph the function.

____ 6. y 4x

a. c.

b. d.

Name: ________________________ ID: A

3

Sketch the asymptotes and graph the function.

____ 7. y 5x 1 1

a. c.

b. d.

____ 8. Write an equation for the translation of y 4x that has the asymptotes x = 7 and y = 6.

a. y 4x 6 7 c. y 4

x 7 6

b. y 4x 7 6 d. y 4

x 6 7

Name: ________________________ ID: A

4

____ 9. This graph of a function is a translation of y 4x . What is an equation for the function?

a. y 4x 3 4 c. y 4

x 4 3

b. y 4x 3 4 d. y 4

x 4 3

Find any points of discontinuity for the rational function.

____ 10. y (x 3)(x 5)(x 7)

(x 1)(x 4)a. x = 1, x = 4 c. x = 3, x = –5, x = 7b. x = –1, x = –4 d. x = –3, x = 5, x = –7

____ 11. What are the points of discontinuity? Are they all removable?

y (x 7)(x 3)x 2 10x 21

a. x = 1, x = –8, x = –2; yes c. x = –7, x = –3; nob. x = 7, x = 3; yes d. x = –1, x = 8, x = 2; no

____ 12. Describe the vertical asymptote(s) and hole(s) for the graph of y x 1x2 6x 8

.

a. asymptotes: x = –4, –2 and hole: x = 1b. asymptote: x = 1 and no holesc. asymptote: x = 1 and holes: x = –4, –2d. asymptotes: x = –4, –2 and no holes

Name: ________________________ ID: A

5

____ 13. Find the horizontal asymptote of the graph of y 2x 3 3x 22x 3 6x 2

.

a. y = 1 c. no horizontal asymptoteb. y = 1 d. y = 0

What is the graph of the rational function?

____ 14. y 2x 4x 1

a. c.

b. d.

Simplify the rational expression. State any restrictions on the variable.

____ 15. t2 4t 32t 8

a. t 4; t 8 c. t 4; t 8b. t 4; t 8 d. t 4; t 8

Name: ________________________ ID: A

6

____ 16. n 4 10n 2 24n 4 9n 2 18

a. n 2 4n 2 3

; n 6 , n 3 c. n 2 4n 2 3

; n 6, n 3

b. n 2 4n 2 3

; n 6, n 3 d.(n 2 4)

n 2 3; n 6 , n 3

What is the product in simplest form? State any restrictions on the variable.

____ 17. 3g 5

10h 2 h 5

10g 2

a.3g 3 h 3

100, g 0, h 0 c.

3g 7

100h 7 , g 0, h 0

b. 1003g 3 h 3 , g 0, h 0 d. 3

100g 7 h 7 , g 0, h 0

____ 18. y 2

y 3 y 2 y 6

y 2 1y

a.y2 2yy 1 , y 3, 1 c.

y 2y 1 , y 3, 0, 1

b.y2 2yy 1 , y 3, 0, 1 d.

y 2y 1 , y 3, 1

What is the quotient in simplified form? State any restrictions on the variable.

____ 19. a 2a 5 a 1

a 2 8a 15

a.(a 2)(a 3)

a 1 , a 5, 1, 3 c.(a 2)(a 3)

a 1 , a 3, 1

b.(a 2)(a 1)(a 5)2(a 3)

, a 5, 3, 1 d.(a 2)(a 1)(a 5)2 (a 3)

, a 5, 3

____ 20. Find the least common multiple of x2 7x 6 and x2 3x 4.a. (x 6)(x 1)(x 4) c. (x 6)(x 4)(x 1)b. (x 1)(x 4)(x 6) d. (x 6)(x 1)(x 4)

Name: ________________________ ID: A

7

Simplify the sum.

____ 21. 4m 9 5

m2 81

a. 9(m 9)(m 9)

c. 9m2 m 72

b. 4m 31(m 9)(m 9) d. 4m 41

(m 9)(m 9)

____ 22. d 2 d 30d 2 3d 40

d 2 14d 48d 2 2d 48

a. 2d 2 15d 182d 2 d 88

c. 2d 2 14d 16(d 8)(d 8)

b. d 2 14d 16(d 8)(d 8) d. 2d 2 15d 18

(d 8)(d 8)

Simplify the difference.

____ 23. n 2 10n 24n 2 13n 42

9n 7

a. n 13n 7 c. n 13

b. n 4n 7 d. n 2 10n 15

n 2 13n 42

____ 24. z2 11z 30z2 z 20

z2 2z 24z2 9z 18

a. z 34(z 4)(z 3) c. 2z2 2

(z 4)(z 3)

b. 17z 2(z 4)(z 3) d. 2z2 8z 34

2z2 34

Simplify the complex fraction.

____ 25.

4x 31x 3

a. 12x 4x2 3x

c. 4x3x 2 10x 3

b. 4x3x 9 d. not here

Name: ________________________ ID: A

8

____ 26.

y 1y 2 y 6

y 6y 3

a.(y 1)(y 6)(y 3)2(y 2)

c.(y 1)(y 6)(y 3)(y 2)

b.y 1

(y 6)(y 2) d.(y 1)(y 2)(y 6)(y 2)

Solve the equation. Check the solution.

____ 27. 4x 1 1

x 5

a. 194 b. 1

3 c. 193 d. 2

____ 28. aa 2 36

2a 6 1

a 6a. –9 b. –6 c. –9 and –6 d. 6

____ 29. 6x2 9

1x 3 1

a. 4 b. 2 c.1 73

2d. 3 or –4

____ 30. A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Kaitlin can paint a certain room in 3 hours. Brianna can paint the same room in 7 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.

a. 3x 7

x 1; 10 hours c. 3x 7

x 1; 5 hours

b. x7 x

3 1; 5 hours d. x3 x

7 1; 2.1 hours

ID: A

1

Algebra 2 - Chapter 8 ReviewAnswer Section

1. ANS: B PTS: 1 DIF: L2 REF: 8-1 Inverse VariationOBJ: 8-1.1 To recognize and use inverse variation NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 1 Identifying Direct and Inverse Variations KEY: inverse variation

2. ANS: C PTS: 1 DIF: L2 REF: 8-1 Inverse VariationOBJ: 8-1.1 To recognize and use inverse variation NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 2 Determining an Inverse Variation KEY: inverse variation

3. ANS: D PTS: 1 DIF: L3 REF: 8-1 Inverse VariationOBJ: 8-1.1 To recognize and use inverse variation NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 2 Determining an Inverse Variation KEY: inverse variation

4. ANS: D PTS: 1 DIF: L4 REF: 8-1 Inverse VariationOBJ: 8-1.2 To use joint and other variations NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 4 Using Combined Variation KEY: inverse variation | combined variation | joint variation

5. ANS: D PTS: 1 DIF: L4 REF: 8-1 Inverse VariationOBJ: 8-1.2 To use joint and other variations NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 5 Applying Combined Variation KEY: combined variation | joint variation

6. ANS: C PTS: 1 DIF: L2 REF: 8-2 The Reciprocal Function Family OBJ: 8-2.1 To graph reciprocal functionsNAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c TOP: 8-2 Problem 1 Graphing an Inverse Variation Function KEY: reciprocal function

7. ANS: C PTS: 1 DIF: L3 REF: 8-2 The Reciprocal Function Family OBJ: 8-2.2 To graph translations of reciprocal functions NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c TOP: 8-2 Problem 3 Graphing a Translation KEY: reciprocal function

8. ANS: C PTS: 1 DIF: L2 REF: 8-2 The Reciprocal Function Family OBJ: 8-2.2 To graph translations of reciprocal functions NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c TOP: 8-2 Problem 4 Writing the Equation of a Transformation KEY: reciprocal function

9. ANS: D PTS: 1 DIF: L3 REF: 8-2 The Reciprocal Function Family OBJ: 8-2.2 To graph translations of reciprocal functions NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c TOP: 8-2 Problem 4 Writing the Equation of a Transformation KEY: reciprocal function

10. ANS: B PTS: 1 DIF: L2 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 1 Finding Points of Discontinuity KEY: rational function | point of discontinuity | removable discontinuity | non-removable points of discontinuity

ID: A

2

11. ANS: B PTS: 1 DIF: L2 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 1 Finding Points of Discontinuity KEY: rational function | point of discontinuity | removable discontinuity | non-removable points of discontinuity

12. ANS: D PTS: 1 DIF: L2 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 2 Finding Vertical Asymptotes KEY: rational function

13. ANS: B PTS: 1 DIF: L3 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 3 Finding Horizontal Asymptotes KEY: rational function

14. ANS: B PTS: 1 DIF: L2 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.2 To graph rational functionsNAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 4 Graphing Rational Functions KEY: rational function

15. ANS: B PTS: 1 DIF: L2 REF: 8-4 Rational ExpressionsOBJ: 8-4.1 To simplify rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 1 Simplifying a Rational Expression KEY: rational expression | simplest form

16. ANS: A PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.1 To simplify rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 1 Simplifying a Rational Expression KEY: rational expression | simplest form

17. ANS: A PTS: 1 DIF: L2 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 2 Multiplying Rational Expressions KEY: rational expression | simplest form

18. ANS: B PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 2 Multiplying Rational Expressions KEY: rational expression | simplest form

19. ANS: A PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 3 Dividing Rational Expressions KEY: rational expression | simplest form

20. ANS: A PTS: 1 DIF: L2 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 1 Finding the Least Common Multiple

ID: A

3

21. ANS: B PTS: 1 DIF: L2 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 2 Adding Rational Expressions

22. ANS: C PTS: 1 DIF: L3 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 2 Adding Rational Expressions

23. ANS: A PTS: 1 DIF: L3 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 3 Subtracting Rational Expressions

24. ANS: B PTS: 1 DIF: L4 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 3 Subtracting Rational Expressions

25. ANS: C PTS: 1 DIF: L3 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 4 Simplifying a Complex Fraction KEY: complex fraction

26. ANS: B PTS: 1 DIF: L3 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 4 Simplifying a Complex Fraction KEY: complex fraction

27. ANS: C PTS: 1 DIF: L2 REF: 8-6 Solving Rational EquationsOBJ: 8-6.1 To solve rational equations NAT: CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11TOP: 8-6 Problem 1 Solving a Rational Equation KEY: rational equation

28. ANS: A PTS: 1 DIF: L4 REF: 8-6 Solving Rational EquationsOBJ: 8-6.1 To solve rational equations NAT: CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11TOP: 8-6 Problem 1 Solving a Rational Equation KEY: rational equation

29. ANS: A PTS: 1 DIF: L3 REF: 8-6 Solving Rational EquationsOBJ: 8-6.1 To solve rational equations NAT: CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11TOP: 8-6 Problem 1 Solving a Rational Equation KEY: rational equation

30. ANS: D PTS: 1 DIF: L3 REF: 8-6 Solving Rational EquationsOBJ: 8-6.2 To use rational equations to solve problems NAT: CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11TOP: 8-6 Problem 2 Using Rational Equations KEY: rational equation