College Algebra - Unit 2 Practice Exam - Fall 2014 Printed Name________________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.1) 1)

A) function B) not a function

Find the domain and range.2) {(-9, -4), (12, -8), (-4, 2), (-2, -7)} 2)

A) D = {-2, 12, -4, -9}; R = { -8, 2, -4} B) D = {-7, -8, 2, -4}; R = {-2, 12, -4, -9}C) D = {-2, 12, -4, -9}; R = {-7, 4, -8, 2, -4} D) D = {-2, 12, -4, -9}; R = {-7, -8, 2, -4}

3) y = x+9 3)A) D = (- , ); R = (- , ) B) D = (- , ); R = [-9, )C) D = [-9, ); R = [0, ) D) D = [0, ); R =[0, )

Use the graph to determine the function's domain and range.4) 4)

A) domain: (- , )range: [2, 5]

B) domain: [0, 5]range: (- , )

C) domain: (- , )range: [0, 5]

D) domain: [2, 5]range: (- , )

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5) 5)

A) domain: [-2, )range: [-2, )

B) domain: (- , )range: (- , )

C) domain: (- , -2) or (-2, )range: (- , -2) or (-2, )

D) domain: (- , )range: [-2, )

Identify the intervals where the function is changing as requested.6) Increasing 6)

A) (-2, 1) B) (-1, 3) C) (-2, -1) or (3, ) D) (-1, )

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7) Increasing 7)

A) (1, 6) B) (0, 6) C) (0, 5) D) (1, 5)

8) Decreasing 8)

A) (6, 12) B) (6, 1) C) (5, 12) D) (5, 1)

Graph the function.

9) f(x) =x + 1 if -8 x < 3-9 if x = 3-x + 4 if x > 3

9)

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A) B)

C) D)

Based on the graph, find the range of y = f(x).

10) f(x) =4 if -4 x < -2|x| if -2 x < 83

x if 8 x 12

10)

A) [0, 8] B) [0, 3

12] C) [0, ) D) [0, 8)

Evaluate the piecewise function at the given value of the independent variable.

11) f(x) = x + 2 if x > -5-(x + 2) if x -5

; f(-6) 11)

A) 4 B) -4 C) -19 D) -6

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Solve the problem.12) Suppose that a rectangular yard has a width of x and a length of 3x. Write the perimeter P as a

function of x.12)

A) P = 8x2 B) P = 4x C) P = 8x D) P = 3x2

Write the equation of the graph after the indicated transformation(s).13) The graph of y = x is vertically stretched by a factor of 2.8. This graph is then reflected across the

x-axis. Finally, the graph is shifted 0.78 units downward.13)

A) y = -2.8 x - 0.78 B) y = 2.8 x - 0.78C) y = 2.8 x - 0.78 D) y = 2.8 -x - 0.78

14) The graph of y = x is translated 4 units to the right. 14)A) y = x + 4 B) y = x - 4 C) y = x - 4 D) y = x + 4

Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.15) g(x) = - f(x) + 2

y = f(x)

15)

A) B)

C) D)

5

Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the givenfunction.

16) h(x) = (x + 3)2 + 6 16)

A) B)

C) D)

Evaluate the piecewise function.

17) f(x) = x - 1 if x > -3-(x - 1) if x -3

determine f(-6) 17)

A) -6 B) -20 C) -7 D) 7

18) g(x) =x2 + 6x + 7

if x -7

x - 5 if x = -7

determine g(-4) 18)

A) -4 B) 23

C) -9 D) 223

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19) h(x) =x2 - 3x - 5

if x 5

x + 8 if x = 5

determine h(5) 19)

A) -3 B) undefined C) 13 D) -13

Given functions f and g, perform the indicated operations.20) f(x) = 4x - 3, g(x) = 3x + 5

Find fg.20)

A) 7x2 + 11x + 2 B) 12x2 + 11x - 15 C) 12x2 - 4x - 15 D) 12x2 - 15

21) f(x) = 9x2 - 7x, g(x) = x2 - 3x - 28

Find fg

.

21)

A) 9xx + 1

B) 9 - x28

C) 9x2 - 7xx2 - 3x - 28

D) 9x - 7-3

Given functions f and g, determine the domain of f + g.

22) f(x) = 4xx - 6

, g(x) = 5x + 9

22)

A) (- , -6) or (-6, 9) or (9, ) B) (- , -9) or (-9, 6) or (6, )C) (- , -5) or (-5, -4) or (-4, ) D) (- , )

23) f(x) = 3x2 - 9, g(x) = 2x3 + 5 23)A) (- , 0) or (0, ) B) (- , -3) or (-3, -2) or (-2, )C) (0, ) D) (- , )

Find the domain of the indicated combined function.

24) Find the domain of fg

(x) when f(x) = 8x2 - 8x and g(x) = x2 - 8x - 7. 24)

A) Domain: - , 4 - 23 4 - 23, 4 + 23 4 + 23,B) Domain: - , 4 - 23 4 - 23, 4 + 23 4 - 23,C) Domain: - , 4 - 23 4 - 23,D) Domain: (- , )

25) Find (f/g)(-2) given f(x) = 3x - 1 and g(x) = 5x2 + 14x + 2. 25)

A) - 12 B) -

56 C) -

76 D)

76

For the given functions f and g , find the indicated composition.

26) f(x) = x - 32

, g(x) = 2x + 3

(g f)(x)

26)

A) x B) x + 6 C) x - 32

D) 2x + 3

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27) f(x) = -3x + 3, g(x) = 6x + 7(g f)(x)

27)

A) -18x + 24 B) -18x + 25 C) 18x + 25 D) -18x - 11

28) f(x) = 8x - 6

, g(x) = 23x

(f g)(x)

28)

A) 8x2 - 18x

B) 2x - 1224x

C) 24x2 - 18x

D) 24x2 + 18x

Use synthetic division or long division to find the quotient and remainder when the first polynomial is divided by thesecond.

29) (x2 - 2x + 4) divided by (x - 5) 29)A) Q: x + 3; R: 19 B) Q: x + 3;R: 15 C) Q: x - 3; R: -19 D) Q: x - 3;R: -15

30) (x5 - 1) divided by (x - 1) 30)A) Q: x4 + x3 + x2 + x + 1; R: 0 B) Q: x5 + x4 + x3 + x2 + x + 1; R: x - 1

C) Q: x5 + x4 + x3 + x2 + x + 1; R: 0 D) Q: x4 + x3 + x2 + x + 1; R: x - 1

31) x5 + x3 + 5x - 2

31)

A) x4 + 2x3 + 4x2 + 9x + 18 +41

x - 2B) x4 + 2x3 + 5x2 + 10x + 20 +

45x - 2

C) x4 + 3 +11

x - 2D) x4 + 3x2 +

11x - 2

32) x4 + 3x3 + x2 + 4x + 2x + 1

32)

A) x3 + 2x2 + x + 5 +6

x + 1B) x3 + 2x2 + x + 3 +

6x + 1

C) x3 - 2x2 - x + 3 -3

x + 1D) x3 + 2x2 - x + 5 -

3x + 1

33) (3x5 - 2x4 - 2x3 + x2 - x + 6) ÷ (x + 1) 33)

A) 3x4 - 5x3 + 3x2 + 2x + 1 +5

x + 1B) 3x4 - 5x3 + 3x2 - 3x - 2 +

8x + 1

C) 3x4 - 5x3 + 3x2 - 3x + 2 +8

x + 1D) 3x4 - 5x3 + 3x2 - 2x - 2 +

5x + 1

34) 5x3 - 137x + 60x - 5

34)

A) 5x2 + 112x + -500x - 5

B) 5x2 - 112x + -500x - 5

C) 5x2 + 25x - 12 D) 5x2 - 25x - 12

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35) 2r3 + 4r2 - 9r - 14r - 2

35)

A) r2 + 7r + 8 B) 2r2 + 8r + 7 C) 2r2 + 8r + 7r - 2

D) 2r2 - 8r - 7

36) Solve the equation 2x3 - 19x2 + 38x + 24 = 0 given that 4 is a zero of f(x) = 2x3 - 19x2 + 38x + 24. 36)

A) 4, -1, 3 B) 4, 1, - 3 C) 4, -6, 12 D) 4, 6, - 1

2

Use the Rational Zero Theorem to list all possible rational zeros for the given function.37) f(x) = x5 - 2x2 + 3x + 3 37)

A) ± 1, ± 3 B) ±12

, ± 32

, ± 3 C) ± 1, ± 13

D) ± 3, ± 13

38) f(x) = x5 - 6x2 + 2x + 10 38)

A) ± 1, ± 5, ± 2, ± 10 B) ± 1, ± 5, ± 2

C) ± 1, ± 15

, ± 12

, ± 110

, ± 5, ± 2, ± 10 D) ± 1, ± 15

, ± 12

, ± 110

39) f(x) = 7x3 - x2 + 3 39)

A) ±13

, ± 73

, ± 1, ± 7 B) ±17

, ± 37

, ± 1, ± 3

C) ±17

, ± 37

, ± 1, ± 3, ± 7 D) ±17

, ± 13

, ± 1, ± 3, ± 7

40) f(x) = -4x4 + 2x2 - 3x + 6 40)

A) ±16

, ± 12

, ± 13

, ± 23

, ± 43

, ± 1, ± 2, ± 4 B) ±14

, ± 12

, ± 34

, ± 32

, ± 1, ± 2, ± 3, ± 6

C) ±14

, ± 12

, ± 34

, ± 32

, ± 1, ± 2, ± 3, ± 4, ± 6 D) ±14

, ± 12

, ± 23

, ± 34

, ± 32

, ± 1, ± 2, ± 3, ± 6

41) f(x) = 6x4 + 3x3 - 6x2 + 3x - 5 41)

A) ± 1, ± 5, ± 12

, ± 52

, ± 13

, ± 53

, ± 16

, ± 56

B) ± 1, ± 2, ± 3, ± 6, ± 12

, ± 52

, ± 13

, ± 53

, ± 16

, ± 56

C) ± 1, ± 5, ± 15

, ± 25

, ± 35

, ± 65

D) ± 1, ± 2, ± 3, ± 6, ± 15

, ± 25

, ± 35

, ± 65

State the degree of the polynomial equation.42) 2(x + 8)2(x - 8)3 = 0 42)

A) 5 B) 3 C) 2 D) 6

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Find a polynomial equation with real coefficients that has the given roots.43) 0, -1, 7 43)

A) x3 + 6x2 - 7x = 0 B) x2 + 6x + 7 = 0C) x3 - 6x2 - 7x = 0 D) x3 - 7x = 0

Find an nth degree polynomial function with real coefficients satisfying the given conditions.44) n = 4; 2i, 3, and -3 are zeros; leading coefficient is 1 44)

A) f(x) = x4 + 4x2 - 3x - 36 B) f(x) = x4 - 5x2 - 36C) f(x) = x4 + 4x3 - 5x2 - 36 D) f(x) = x4 + 4x2 - 36

45) n = 3; 3 and i are zeros; f(2) = 25 45)A) f(x) = -5x3 + 15x2 - 5x + 15 B) f(x) = 5x3 - 15x2 + 5x - 15C) f(x) = 5x3 - 15x2 - 5x + 15 D) f(x) = -5x3 + 15x2 + 5x - 15

46) n = 3; - 5 and i are zeros; f(-3) = 60 46)A) f(x) = 3x3 + 15x2 + 3x + 15 B) f(x) = -3x3 - 15x2 - 3x - 15C) f(x) = 3x3 + 15x2 - 3x - 15 D) f(x) = -3x3 - 15x2 + 3x + 15

Find all of the real and imaginary zeros for the polynomial function.47) f(x) = x3 - 6x2 + x - 6 47)

A) -6, 6, i B) 6, -i, i C) -6, -i, i D) -1, 1, 6

Find a rational zero of the polynomial function and use it to find all the zeros of the function.48) f(x) = x3 + 8x2 + 14x + 4 48)

A) {-2, -3 + 7, -3 - 7} B) {2, -6 + 7, -6 - 7}C) {1, -1, -4} D) {-2, -6 + 4, -6 - 4}

49) f(x) = 3x3 - x2 - 18x + 6 49)

A) {3, 6, - 6} B) {- 13

, 6, - 6} C) {-3, 6, - 6} D) { 13

, 6, - 6}

Solve the absolute value equation or indicate that the equation has no solutions.50) x - 2 = 5 50)

A) {-7} B) {-3, 7} C) {3, 7} D) No Solutions

51) 6x - 7 + 4 = 1 51)

A)23 B)

23 , -

53 C) 5

3, - 2

3D) No Solutions

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Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solutionset on a number line.

52) |x - 1| > 0 52)

A) (-1, 1)

B) (1, )

C) (- , 1) (1, )

D)

53) |x - 5| 0 53)

A) (- , )

B) (-5, 5)

C) (5, )

D) {5}

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54) |x + 7| + 5 7 54)

A) (- , -9] [-5, )

B) [-9, 7]

C) [-9, -5]

D) (-9, -5)

55) 4y + 123

< 4 55)

A) (-6, 0) B) (- , -6) (6, )

C) (-6, 6) D) (- , -6) (0, )

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Answer KeyTestname: CA UNIT 2 PRACTICE EXAM FALL 2014V3

1) B2) D3) C4) C5) D6) C7) C8) C9) D

10) D11) A12) C13) A14) B15) A16) A17) D18) D19) C20) B21) C22) B23) D24) A25) D26) A27) B28) C29) A30) A31) B32) D33) A34) C35) B36) D37) A38) A39) B40) B41) A42) A43) C44) B45) A46) A47) B48) A49) D50) B

51) D52) C53) A54) C55) A

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