Name ______________________
Date _____________________
Pre-Calculus Midterm Review
Do This on Another Sheet of Paper!
SHOW WORK TO RECEIVE CREDIT!!
1. Given: P( x)  x3  3x 2  16 x  12 . Find: P(-2)
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2. The graph of y  2  f ( x) is
a. A reflection of the graph of y=f(x) over the x-axis
b. A vertical shrink of the graph of y=f(x)
c. A vertical stretch of the graph of y=f(x)
d. A reflection of the graph of y=f(x) over the y-axis
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Describe if the following functions are odd, even, or neither.
3.
f ( x)  x
4. f ( x) 
3
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5. f ( x)  x 2  2
x
6. Let f ( x) 
x and g ( x)  6 x  3 , find g ( f ( x)) .
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7. Let f ( x) 
x and g ( x)  6 x  3 , find f ( g ( x)) .
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Give the domain and range of the following functions.
8.
y
x4
x2  4
9. y 
x  5 1
10. y  ( x  2)2  4
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11. y 
2x  5
4x  3
12. In which quadrant is cos   0 and tan   0 ?
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13. The value of cosine is negative which quadrants?
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14. Convert 120˚ to radian measure.
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15. Convert

to degrees.
4
16. Find an angle that is coterminal to
17. Evaluate cos
5
.
3
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9
.
4
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Which of the following functions has an inverse that is a function?
18. f ( x) 
3
19. f ( x)  x 4
x
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20. f ( x)  x 2
Find the inverse of the relation.
21. f ( x) 
1
x4
3
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22. f ( x)  5x  5
23. f ( x)  ( x  4)3  2
24. Find the range of f ( x)  3  x 2 .
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25. Find the range of f ( x) 
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x3 .
26. Determine the slope and y-intercept for the equation 2x+5y+8=0.
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27. The value of sine is negative in which quadrants?
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28. Convert 220˚ to radian measure.
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29. The vertical line test is a test given to the graph of a relation to
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determine if the
a. Relation is a function
b. Relation is a one-to-one function
c. Relation is a constant
d. Relation is an even function
30. The horizontal line test is a test given to the graph of a function
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to decide if the
a. Function is a constant
b. Function is an even function
d. Function is a relation
d. Function is a one-to-one function
31. Which of the following is not a function?
a.
y
1
x 3
b. y  3
c. x 2  y 2  1
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d. y  x  2
32. Given that csc  0 and cot   0 ,  is in which quadrant?
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33. Given that sin   0 and cos   0 ,  is in which quadrant?
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34. Given that sec  0 and tan   0 ,  is in which quadrant?
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35. Determine the equation of the line which passes through the
point (2,6) and is also perpendicular to the line y=1.
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36. Write the equation of the line that passes through the
two points (2,1) and (1,6) in slope-intercept form.
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37. Write an equation of the line that passes through (-2,1) and is
perpendicular to the line y 
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1
x 1 .
2
38. Write an equation of the line that passes through (5,5) and is
parallel to the line 2x-2y= -3.
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Graph each of the following functions and determine the Domain, Range,
and any asymptotes. You may use the graphing grids on the back of this
review to graph these.
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39. f ( x) 
x 3
x2
43. f ( x) 
1
( x  1) 2  5
2
40. y 
4x  3
x4
41. f ( x) 
44. y  2( x  2)2  7
x6
45. y   x 2  4 x  1
Write a polynomial function, in standard form, of least degree that has
real coefficients, the given zeros, and a leasing coefficient of 1.
46. -1, -2, -3
47. -2,
3
0
x2
51. 5  2 x 2  9 x
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49. 3x2  4 x  15  0
52.
50.
x 1
0
x4
6
0
x 1
Write a quadratic function in vertex form that has the given vertex and
passes through the given point.
53. V(-2, 5), P(0, -3)
54. V(0, 0), P(3, 3)
55. V(4, -4), P(2, 6)
56. V(1, -8), P(-2, 10)
Determine the vertex of the parabola.
56. y  3x 2  12 x  8
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5 ,- 5
Solve the following inequalities.
48.
42. y  x 2  2 x  3
57. y  4  6 x  2 x 2
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58. y  2 x x  8x  3
Find the x- and y- intercepts.
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60. y  x 2  5x  6
59. 5x  4 y  20
If f ( x)  x 2 , g ( x)  3x , and h( x)  x  1 , then find:
61. f ( g (1))
62. (h( g ( f (3)))
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63. g ( f (
1
))
2
64. Evaluate f (2) .
 x  2 x
f ( x)  
2 x  3
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2
,
x 1
x 1
65. Evaluate f (6) .
1  2 x
f ( x)   2
2 x
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,
x2
x2
66. A 22-ft flagpole casts a 62-ft shadow. Calculate
(to the nearest degree) the angle of elevation to the sun.
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67. If a guy wire for a tree is 14 ft long, making a 41˚ angle with the
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ground, how far is the base of the tree from the stake anchoring the wire?
Determine the end behavior for each of the following functions.
68. f ( x)  4 x  x3
69. f ( x)  6 x 4  24 x3
71. f ( x)  15x13  x10  7 x9  x15  11x  9
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70. f ( x)  ( x  1)2
72. f ( x)   x 2  3x
73. Tell whether #70 and #72 have a maximum or a minimum.
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74. Determine the real zeros (or roots) of f ( x)  x3  2 x 2  x  2
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75. Determine the remaining zeros of f ( x)  x3  5x 2  2 x  24
if x=3 is a zero.
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Factor the function completely given one of the zeros.
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76. f ( x)  x3  x 2  6 x , x=2
77. f ( x)  2 x3  3x 2  5x  6
, x= -1
Find the exact value for each of the following trig functions.
78. tan 330˚
82. sin
79. csc (-405 ˚)
13
6
83. sec
11
3
80. cos 150 ˚
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81. sin (-840 ˚)
 8 

 3 
84. cot  
85. cos
7
4
Without graphing, find the amplitude and period.
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86. y  5cos 1 x
2
87. y  3sin 4 x
88. y  4cos  2  x 
89. y  2sin  2 x 
Graph. You may use the graphing grids on the back of this
review to graph these.
90. y  2  sin( x)
92. y  3cos( x   )
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

93. y  2 tan  x 
Find the reference angle of each the given angles.
94. 120˚
95. -475 ˚
96.
7
4

 1
4
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97.
13
6
Below are graphing grids for #39-45, and #90-93.
39.
40.
41.
42.
43.
44.
45.
90.
91.
92.
93.