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Pre-Calculus Honors
Final Exam Review
Name:
Determine the domain of the function given.
1. 𝑓(𝑥) = √𝑥 + 4
2. 𝑓(𝑥) = √9 − 𝑥
3. 𝑓(𝑥) =
𝑥+2
𝑥−1
Determine whether the equation defines y as a function of x.
5. 5x – 4y3 = 64
6. 2y2 + x = 3
7. 10x + 6 = 2y
4. 𝑓(𝑥) = 𝑥 2 + 4𝑥 − 5
8. 4x + 2 = 4y2
Determine whether the graph is a function.
9.
10.
11.
12.
For questions 13 – 16: the graph on the right
defines a function f.
13. Evaluate f(4)
14. Evaluate f(-2)
15. Give the range of f(x)
16. Give the domain of f(x)
What is the vertex of the quadratic function? Then, describe the transformation of the graph
f(x) = x2.
17. f(x) = -(x – 4)2 + 5
18. f(x) = ½(x – 3)2 – 3
19. f(x) = -(x + 2)2 – 3
20. f(x) = -5(x + 2)2
State whether the function f(x) is a reflection of g(x) over:
A. the line y = x ; B. the x-axis ; C. the y-axis ; D. the origin
21. f(x) = 9x – 1 ; g(x) =
𝑥+1
9
23. f(x) = ½x + 2 ; g(x) = 2x – 4
22. f(x) = 2x2 + 9 ; g(x) = -2x2 – 9
24. f(x) = 3(x + 2)2 ; g(x) = 3(-x - 2)2
25. Match the correct graph with the function f(x) = (x – 2)2 + 6
A.
B.
C.
D.
26. Match the correct graph with the function f(x) = (x + 4)2 – 2
A.
B.
C.
D.
27: A rocket is fired upward from a platform 10
feet above the ground (initial height is 10 feet)
with an initial velocity of 1500 ft/sec. Determine
the rocket’s maximum height. Use the equation s
= -16t2 + vot + so for the height (in feet) of the
rocket along a vertical line after t seconds.
27. A rocket is fired upward from a platform 15
feet above the ground (initial height is 15 feet)
with an initial velocity of 1000 ft/sec. Determine
the rocket’s maximum height. Use the equation
s = -16t2 + vot + so for the height (in feet) of the
rocket along a vertical line after t seconds.
Given f(x) and g(x), find (f ○ g)(x).
28. f(x) = 5x + 1 ; g(x) = 3x
29. f(x) = x2 – 2x + 1 ; g(x) = 2x
Find the quotient and remainder when f(x) is divided by g(x).
30. f(x) = x5 – x3 + x – 5 ; g(x) = x – 2
31. f(x) = x3 + 3x2 – 6x + 20 ; g(x) = x + 5
Find all the zeros of f(x).
32. f(x) = -2x2 + 2x – 8
33. f(x) = x3 – 2x2 – 7x – 4
34. f(x) = x3 – x2 + 4x – 4
35. f(x) = x4 + 3x3 – 2x2 – 12x - 8
36. Write a 4th degree polynomial with integer coefficients that has the roots 2i, 2, and 1.
37. Write a 3rd degree polynomial with integer coefficients that has the roots -2, 3, and 0.
38. Using the piece-wise function (𝑥) =
1 2
𝑥
{2
− 2 𝑓𝑜𝑟 𝑥 ≥ 4
√4 − 𝑥 𝑓𝑜𝑟 𝑥 < 4
, find 𝑓(4) and 𝑓(−4).
39. Give intervals for which f(x) is increasing: f(x) = x4 – 3x2 + 1
40. If a 65 foot ladder leans against a building with an angle of elevation of 25°, how far away from the
building is the ladder?
41. If a building is 75 feet tall and casts a shadow that is 50 feet long, what is the angle of depression of
the building?
42. If the angle of elevation of the sun is 47° and the tree is 30 feet tall, how long of a shadow will it cast?
1 −5
43. Write in exponential form: ln 4 = 1.386
44. Write in logarithmic form: (4)
Solve the exponential or logarithmic equation.
47. 5 − 𝑒 3𝑥 = −40
48. 𝑙𝑜𝑔16 3 = 𝑥
= 1024
49. log 4 𝑥 + log 4 (𝑥 − 6) = 2
50. log(6 − 𝑥) + log 3 = log 𝑥
Find the exact value of the following.
51. sin 135°
−√3
)
2
52. cot 300°
53. sin−1 (
55. Change 7π/18 into degrees.
54. tan-1(1)
56. Change 210° into radians.
57. Find tan θ when sin θ = -½ in Quadrant III.
58. Find the Quadrant II angle whose reference angle is 17°.
59. The sides of an isosceles triangle are a = 6, b = 12, and c = 12. Find angle A.
60. Let angle A = 35°, angle B = 104°, and side c = 75. What is side b?
61. If A = 32°, B = 90°, and c = 15, what is a?
62. The angle of depression from the top of a 110 feet lighthouse to ship A is 12 degrees while the angle of
depression to ship B is 7 degrees. Find the distance between the 2 ships.
63. Solve √2sin x – 5 = -4.
64. Solve 2 tan x + 6 = 8.
65. What is a positive coterminal angle with -310°?
66. Give the exact value of the cos(𝜃) ratio when the terminal side of θ passes through the point (4 , 3).
State the transformations on the trigonometric function and graph.
67. −5 sin (𝑥 +
3𝜋
)
4
+ 3
𝜋
68. −2 cos (2𝑥 + 2 )