ExamView - PreCalc Semester 1 Final Exam Revie · 12/1/2015 · PreCalculus: Semester 1 Final Exam...
Transcript of 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.
6. Find the value for the function.
Find f(4) when f(x) = .
7. Find the value for the function.
Find -f(x) when f(x) = 2x2 - 3x + 4.
8. Find the value for the function.
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.
12. For the given functions f and g, find the
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.
22. The graph of a function is given. Decide whether
it is even, odd, or neither.
23. 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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27. Graph the function.
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
33. 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 B
34. 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 B) C
35. 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.
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
39. 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.
(x9y-1)3
40. 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.
(x-6y6)-7z9
41. 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.
-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
48. Find the quotient and the remainder.
6x2 + 17x - 28 divided by x + 4
49. Find the quotient and the remainder.
x4 + 6x2 + 7 divided by x2 + 1
50. Factor completely. If the polynomial cannot be
factored, say it is prime.
9x2 - 1
51. Factor completely. If the polynomial cannot be
factored, say it is prime.
27y3 - 1
52. Factor completely. If the polynomial cannot be
factored, say it is prime.
x2 + 2x + 1
Name: ________________________ ID: A
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53. Factor completely. If the polynomial cannot be
factored, say it is prime.
81x2 - 126x + 49
54. Factor completely. If the polynomial cannot be
factored, say it is prime.
2x2 - 2x - 12
55. Factor completely. If the polynomial cannot be
factored, say it is prime.
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))
64. For the given functions f and g, find the
requested composite function value.
f(x) = , g(x) = 5x; Find (f g)(3).
65. For the given functions f and g, find the
requested composite function value.
f(x) = 4x + 6, g(x) = 4x2 + 1; Find (g f)(4).
66. For the given functions f and g, find the
requested composite function value.
f(x) = 3x + 8, g(x) = ; Find (g f)(3).
Name: ________________________ ID: A
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67. For the given functions f and g, find the
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) =
104. Graph the function.
f(x) =
105. Graph the function.
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
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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
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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
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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