examview - precalc semester 1 final exam revie · 12/1/2015 · precalculus: semester 1 final exam...

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

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PreCalculus: Semester 1 Final Exam Review

Short Answer

1. Determine whether the relation represents a

function. If it is a function, state the domain and

range.

2. Determine whether the relation represents a

function. If it is a function, state the domain and

range.

{(19, -4), (3, -3), (3, 0), (12, 3), (28, 5)}

3. Determine whether the equation defines y as a

function of x.

y = |x|

4. Determine whether the equation defines y as a

function of x.

y2 = 6 - x2

5. Find the value for the function.

Find f(-9) when f(x) = |x|- 6.


Find f(4) when f(x) = .


Find -f(x) when f(x) = 2x2 - 3x + 4.


Find f(x - 1) when f(x) = 3x2 - 5x - 5.

9. Find the domain of the function.

f(x) = x2 + 4

10. Find the domain of the function.

h(x) =

11. For the given functions f and g, find the

requested function and state its domain.

f(x) = 4x - 3; g(x) = 8x - 9

Find f - g.


requested function and state its domain.

f(x) = 3x + 4; g(x) = 4x - 6

Find f • g.

13. Solve the problem.

Find (f + g)(-2) when f(x) = x - 3 and g(x) = x + 1.

14. Solve the problem.

Find (-3) when f(x) = 3x - 4 and g(x) = 3x2 +

14x + 3.

Name: ________________________ ID: A

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15. Determine whether the graph is that of a

function. If it is, use the graph to find its domain

and range, the intercepts, if any, and any

symmetry with respect to the x-axis, the y-axis,

or the origin.

16. Determine whether the graph is that of a

function. If it is, use the graph to find its domain

and range, the intercepts, if any, and any

symmetry with respect to the x-axis, the y-axis,

or the origin.

17. The graph of a function f is given. Use the graph

to answer the question.

Use the graph of f given below to find f(-6).

18. The graph of a function f is given. Use the graph

to answer the question.

For what numbers x is f(x) = 0?

19. Answer the question about the given function.

Given the function f(x) = -2x2 - 4x - 8, is the point

(-1, -6) on the graph of f?

Name: ________________________ ID: A

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20. Answer the question about the given function.

Given the function f(x) = , is the point (-2, 8)

on the graph of f?

21. The graph of a function is given. Decide whether

it is even, odd, or neither.





24. Determine algebraically whether the function is

even, odd, or neither.

f(x) = -2x4 - x2

25. Determine algebraically whether the function is

even, odd, or neither.

f(x) = -5x2 - 4

26. Graph the function.

f(x) =

Name: ________________________ ID: A

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f(x) =

28. Match the correct function to the graph.

29. Write an equation that results in the indicated

translation.

The absolute value function, shifted 5 units to the

left

30. Write an equation that results in the indicated

translation.

The square root function, shifted 5 units upward

31. Graph the function by starting with the graph

of the basic function and then using the

techniques of shifting, compressing, stretching,

and/or reflecting.

f(x) = (x - 7)2 + 4

32. Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},

A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4,

9} to find the set.

A C


A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4,

9} to find the set.

A B


A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4,

9} to find the set.

(A B) C


A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4,

9} to find the set.

36. Evaluate the expression using the given values.

-3xy + 8y - 5 x = 4, y = 3

Name: ________________________ ID: A

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37. Evaluate the expression using the given values.

x = 7, y = 8

38. Simplify the expression. Express the answer so

that all exponents are positive. Whenever an

exponent is 0 or negative, we assume that the

base is not 0.

(-4x2)-1




base is not 0.

(x9y-1)3




base is not 0.

(x-6y6)-7z9




base is not 0.

-1

42. Tell whether the expression is a polynomial. If it

is, give its degree.

7x2 -

43. Tell whether the expression is a polynomial. If it

is, give its degree.

7z6 + z

44. Add, subtract, or multiply, as indicated.

Express your answer as a single polynomial in

standard form.

8(1 - y3) + 5(1 + y + y2 + y3)

45. Multiply the polynomials using the special

product formulas. Express the answer as a

single polynomial in standard form.

(2x - 10)(2x + 10)

46. Multiply the polynomials using the special

product formulas. Express the answer as a

single polynomial in standard form.

(x - 10)2

47. Find the quotient and the remainder.

9x8 - 15x4 divided by 3x


6x2 + 17x - 28 divided by x + 4


x4 + 6x2 + 7 divided by x2 + 1

50. Factor completely. If the polynomial cannot be

factored, say it is prime.

9x2 - 1



27y3 - 1



x2 + 2x + 1

Name: ________________________ ID: A

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81x2 - 126x + 49



2x2 - 2x - 12



10x2 + 21x + 9

56. Use synthetic division to find the quotient and

the remainder.

x5 + x2 - 4 is divided by x + 3

57. Use synthetic division to find the quotient and

the remainder.

-3x3 - 9x2 + 10x - 8 is divided by x + 4

58. Use synthetic division to determine whether x - c

is a factor of the given polynomial.

x3 - 4x2 - 39x + 126; x + 6

59. Use synthetic division to determine whether x - c

is a factor of the given polynomial.

x3 - 9x2 + 8x + 64; x + 6

60. Reduce the rational expression to lowest terms.

61. Reduce the rational expression to lowest terms.

62. Evaluate the expression using the values given in

the table.

(g f)(1)

63. Evaluate the expression using the values given in

the table.

f(g(-5))


requested composite function value.

f(x) = , g(x) = 5x; Find (f g)(3).



f(x) = 4x + 6, g(x) = 4x2 + 1; Find (g f)(4).



f(x) = 3x + 8, g(x) = ; Find (g f)(3).

Name: ________________________ ID: A

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requested composite function.

f(x) = , g(x) = ; Find (f g)(x).

68. Decide whether the composite functions, f g

and g f, are equal to x.

f(x) = x2 + 1 , g(x) = - 1

69. Decide whether the composite functions, f g

and g f, are equal to x.

f(x) = , g(x) = x2

70. Find functions f and g so that f g = H.

H(x) =

71. Find functions f and g so that f g = H.

H(x) =

72. Find the domain of the composite function f g.

f(x) = x + 9; g(x) =

73. Find the domain of the composite function f g.

f(x) = ; g(x) =

74. Determine whether the function is one-to-one.

75. Indicate whether the function is one-to-one.

{(-20, -18), (10, -18), (-8, 18)}

76. Use the horizontal line test to determine

whether the function is one-to-one.

77. Use the horizontal line test to determine

whether the function is one-to-one.

Name: ________________________ ID: A

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78. Find the inverse of the function and state its

domain and range .

{(-4, -8), (8, 4), (-3, -2), (3, 2)}

79. Graph the function as a solid line or curve and

its inverse as a dashed line or curve on the same

axes.

2y - 10 = 4x

80. Graph the function as a solid line or curve and

its inverse as a dashed line or curve on the same

axes.

f(x) =

81. Decide whether or not the functions are inverses

of each other.

f(x) = 3x + 9, g(x) = x - 3

82. Decide whether or not the functions are inverses

of each other.

f(x) = (x - 4)2, x ≥ 4; g(x) = + 4

83. The function f is one-to-one. Find its inverse.

f(x) = 6x2 - 3, x ≥ 0

84. The function f is one-to-one. Find its inverse.

f(x) =

85. The function f is one-to-one. State the domain

and the range of f and f-1.

f(x) =

86. State whether the function is a polynomial

function or not. If it is, give its degree. If it is

not, tell why not.

f(x) =

87. State whether the function is a polynomial

function or not. If it is, give its degree. If it is

not, tell why not.

f(x) = 11

88. Form a polynomial whose zeros and degree are

given.

Zeros: -3, -2, 2; degree 3

89. Form a polynomial whose zeros and degree are

given.

Zeros: 0, - 3, 2; degree 3

Name: ________________________ ID: A

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90. For the polynomial, list each real zero and its

multiplicity. Determine whether the graph

crosses or touches the x-axis at each x -intercept.

f(x) = 4(x - 7)(x - 5)4

91. For the polynomial, list each real zero and its

multiplicity. Determine whether the graph

crosses or touches the x-axis at each x -intercept.

f(x) = 3(x + 2)(x - 4)3

92. Find the x- and y-intercepts of f.

f(x) = 2x3(x - 2)5

93. Find the x- and y-intercepts of f.

f(x) = (x + 2)(x - 5)(x + 5)

94. Find the domain of the rational function.

G(x) =

95. Find the domain of the rational function.

R(x) =

96. Use the graph to determine the domain and

range of the function.

97. Use the graph to determine the domain and

range of the function.

98. Graph the function using transformations.

f(x) = + 1

Name: ________________________ ID: A

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99. Graph the function using transformations.

f(x) = + 1

100. Find the vertical asymptotes of the rational

function.

f(x) =

101. Find the vertical asymptotes of the rational

function.

f(x) =

102. Give the equation of the horizontal asymptote, if

any, of the function.

h(x) =

103. Give the equation of the oblique asymptote, if

any, of the function.

h(x) =


f(x) =


f(x) =

106. Solve the inequality algebraically. Express the

solution in interval notation.

(x - 5)2(x + 7) > 0

107. Solve the inequality algebraically. Express the

solution in interval notation.

(x + 2)(x - 2)(x - 7) < 0

Name: ________________________ ID: A

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Essay

108. Analyze the graph of the given function f as

follows:

(a) Determine the end behavior.

(b) Find the x–and y–intercepts of the graph.

(c) Determine whether the graph crosses or touches

the x-axis at each x-intercept.

(d) Find the domain of f.

(f) Use the information obtained in (a) – (d) to

draw a complete graph of f by hand.

109. Analyze the graph of the given function f as

follows:

(a) Determine the end behavior.

(b) Find the x–and y–intercepts of the graph.

(c) Determine whether the graph crosses or touches

the x-axis at each x-intercept.

(d) Find the domain of f.

(f) Use the information obtained in (a) – (d) to

draw a complete graph of f by hand.

ID: A

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PreCalculus: Semester 1 Final Exam Review

Answer Section

SHORT ANSWER

1. ANS:

function

domain: {Alice, Brad, Carl}

range: {cat, dog}

PTS: 1

2. ANS:

not a function

PTS: 1

3. ANS:

function

PTS: 1

4. ANS:

not a function

PTS: 1

5. ANS:

3

PTS: 1

6. ANS:

4

PTS: 1

7. ANS:

-2x2 + 3x - 4

PTS: 1

8. ANS:

3x2 - 11x + 3

PTS: 1

9. ANS:

all real numbers

PTS: 1

10. ANS:

{x|x -4, 0, 4}

PTS: 1

ID: A

2

11. ANS:

(f - g)(x) = -4x + 6; all real numbers

PTS: 1

12. ANS:

(f • g)(x) = 12x2 - 2x - 24; all real numbers

PTS: 1

13. ANS:

-6

PTS: 1

14. ANS:

PTS: 1

15. ANS:

not a function

PTS: 1

16. ANS:

function

domain: {x|x > 0}

range: all real numbers

intercept: (1, 0)

symmetry: none

PTS: 1

17. ANS:

0

PTS: 1

18. ANS:

-3, 3.5, 5

PTS: 1

19. ANS:

Yes

PTS: 1

20. ANS:

No

PTS: 1

ID: A

3

21. ANS:

even

PTS: 1

22. ANS:

neither

PTS: 1

23. ANS:

odd

PTS: 1

24. ANS:

even

PTS: 1

25. ANS:

even

PTS: 1

26. ANS:

PTS: 1

ID: A

4

27. ANS:

PTS: 1

28. ANS:

y =

PTS: 1

29. ANS:

y =

PTS: 1

30. ANS:

y = + 5

PTS: 1

31. ANS:

PTS: 1

32. ANS:

{1, 2, 3, 4, 5, 8, 9}

PTS: 1

ID: A

5

33. ANS:

{2, 3, 5}

PTS: 1

34. ANS:

{1, 2, 3, 4, 5, 9}

PTS: 1

35. ANS:

{0, 2, 3, 4, 5, 6, 7, 8, 9}

PTS: 1

36. ANS:

-17

PTS: 1

37. ANS:

PTS: 1

38. ANS:

-

PTS: 1

39. ANS:

PTS: 1

40. ANS:

PTS: 1

41. ANS:

PTS: 1

42. ANS:

Not a polynomial

PTS: 1

ID: A

6

43. ANS:

Polynomial; degree 6

PTS: 1

44. ANS:

-3y3 + 5y2 + 5y + 13

PTS: 1

45. ANS:

4x2 - 100

PTS: 1

46. ANS:

x2 - 20x + 100

PTS: 1

47. ANS:

3x7 - 5x3; remainder 0

PTS: 1

48. ANS:

6x - 7; remainder 0

PTS: 1

49. ANS:

x2 + 5; remainder 2

PTS: 1

50. ANS:

(3x - 1)(3x + 1)

PTS: 1

51. ANS:

(3y - 1)(9y2 + 3y + 1)

PTS: 1

52. ANS:

(x + 1)2

PTS: 1

53. ANS:

(9x - 7)2

PTS: 1

54. ANS:

2(x + 2)(x - 3)

PTS: 1

ID: A

7

55. ANS:

(2x + 3)(5x + 3)

PTS: 1

56. ANS:

x4 - 3x3 + 9x2 - 26x + 78; remainder -238

PTS: 1

57. ANS:

-3x2 + 3x - 2; remainder 0

PTS: 1

58. ANS:

Yes

PTS: 1

59. ANS:

No

PTS: 1

60. ANS:

PTS: 1

61. ANS:

4x - 9

PTS: 1

62. ANS:

-8

PTS: 1

63. ANS:

1

PTS: 1

64. ANS:

3

PTS: 1

65. ANS:

1937

PTS: 1

ID: A

8

66. ANS:

-

PTS: 1

67. ANS:

PTS: 1

68. ANS:

No, no

PTS: 1

69. ANS:

No, no

PTS: 1

70. ANS:

f(x) = ; g(x) = x2 - 4

PTS: 1

71. ANS:

f(x) = ; g(x) = 5x + 4

PTS: 1

72. ANS:

{x

PTS: 1

73. ANS:

{x

PTS: 1

74. ANS:

One-to-one

PTS: 1

75. ANS:

No

PTS: 1

ID: A

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76. ANS:

No

PTS: 1

77. ANS:

Yes

PTS: 1

78. ANS:

{(-8, -4), (4, 8), (-2, -3), (2, 3)} D = {-8, 4, -2, 2}; R = {-4, 8, -3, 3}

PTS: 1

79. ANS:

PTS: 1

80. ANS:

PTS: 1

81. ANS:

Yes

PTS: 1

ID: A

10

82. ANS:

Yes

PTS: 1

83. ANS:

f-1(x) =

PTS: 1

84. ANS:

f-1(x) =

PTS: 1

85. ANS:

f(x): D = {x|x ≠ 2}, R = {y ≠ 0};

f-1(x): D = {x|x ≠ 0}, R = {y|y ≠ 2}

PTS: 1

86. ANS:

Yes; degree 3

PTS: 1

87. ANS:

Yes; degree 0

PTS: 1

88. ANS:

f(x) = x3 + 3x2 - 4x - 12 for a = 1

PTS: 1

89. ANS:

f(x) = x3 + x2 - 6x for a = 1

PTS: 1

90. ANS:

7, multiplicity 1, crosses x-axis; 5, multiplicity 4, touches x-axis

PTS: 1

91. ANS:

-2, multiplicity 1, crosses x-axis; 4, multiplicity 3, crosses x-axis

PTS: 1

92. ANS:

x-intercepts: 0, 2; y-intercept: 0

PTS: 1

ID: A

11

93. ANS:

x-intercepts: -2, -5, 5; y-intercept: -50

PTS: 1

94. ANS:

all real numbers

PTS: 1

95. ANS:

{x|x -9, 4}

PTS: 1

96. ANS:

domain: {x|x 2}

range: {y|y 3}

PTS: 1

97. ANS:

domain: {x|x 0}

range: all real numbers

PTS: 1

98. ANS:

PTS: 1

ID: A

12

99. ANS:

PTS: 1

100. ANS:

x = -3, x = 3

PTS: 1

101. ANS:

x = , x = -1

PTS: 1

102. ANS:

none

PTS: 1

103. ANS:

none

PTS: 1

ID: A

13

104. ANS:

PTS: 1

105. ANS:

PTS: 1

106. ANS:

(- , -7)

PTS: 1

107. ANS:

(- , -2) (2, 7)

PTS: 1

ID: A

14

ESSAY

108. ANS:

PTS: 1

ID: A

15

109. ANS:

PTS: 1

examview - precalc semester 1 final exam revie · 12/1/2015 · precalculus: semester 1 final exam...

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