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Final Exam Review 2016 - Precalculus
Multiple Choice Section [2 points each]
1. Write the slope-intercept form of the equation of the line through the given point perpendicular
to the given line.
point: (–5, 1)
line: –9x - 18y = 4
2. Find all real values of x such that f(x) = 0.
3. Find the difference quotient and simplify your answer.
f(x) = x2 – x + 1,
,h≠0
4. Find the domain of the function.
5. Use a graphing utility to graph the function and visually determine the intervals over which the
function is increasing, decreasing, or constant.
6. Describe the sequence of transformations from the related common function
7. Find (f / g)(x). What is the domain of f / g?
8. Evaluate the indicated function for
and
.
to g.
9. Determine whether the statement is true or false.
The function given by
has no x-intercepts.
10. Find the vertex of the parabolic graph of the equation.
y = 6(x - 8) 2 + 9
11. Use synthetic division to divide.
12. If x = 1 is a root of
, use synthetic division to factor the polynomial
completely and list all real solutions of the equation.
13. Find the domain of the function
.
14. Select the correct rational function for the following graph.
15. Find vertical asymptotes of the following function.
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16. Identify the x-intercept of the function
.
17. Rewrite the logarithm as a ratio of common logarithms.
log5 19
18. Use the properties of logarithms to expand the expression as a sum, difference, and/or
constant multiple of logarithms. (Assume all variables are positive.)
19. Solve for x. Approximate the result to three decimal places.
20. Condense the expression to the logarithm of a single quantity.
21. Solve the exponential equation algebraically. Approximate the result to three decimal places.
22. Solve the logarithmic equation algebraically. Approximate the result to three decimal places.
23. Convert the angle measure from radians to degrees. Round to three decimal places.
24. Determine the quadrant in which an angle, θ, lies if
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.
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25. Using the figure below, if θ = 32° and y = 5, determine the exact value of x.
26. Find (if possible) the complement of the following angle.
27. Find (if possible) the supplement of the following angle.
28. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of
length s.
Radius r
5 inches
Arc Length s
17 inches
29. Given the figure below, determine the value of
30. Find the reference angle
, and sketch
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and
.
in standard position.
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Short Answer Section [5 points each] – Choose 1 of 10
26. Find the zeros: 3𝑥 2 − 13𝑥 − 10 = 0. Leave your answer in exact form.
27. If 𝑓(𝑥) = −𝑥 2 + 2𝑥 − 8 and 𝑔(𝑥) = 3𝑥 + 5 evaluate (𝑓 + 𝑔)(−2)
28. Evaluate the function at each value of the independent variable and simplify:
2𝑥 − 7 𝑥 < 0
𝑓(𝑥) = { 2
𝑥 +3 𝑥 ≥0
a.) 𝑓(−8)
b.) 𝑓(0)
c.) 𝑓(4)
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29. Find the inverse, g(x), of f(x) and use composition to show that ƒ and g are inverses of each
other.
30. Solve for 𝑥: 3 𝑥 = 9 𝑥+8 . Round to the nearest hundredth.
31. Solve ln(4𝑥 − 1) = 𝑙𝑛(𝑥 + 2). Give the exact answer then use a calculator to find an
approximate answer. Eliminate any extraneous solutions.
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32. Use the right triangle below to find B and C.
60°
50
C
B
33. Use trigonometric identities or a right triangle to fine sin
standard position if 𝑡𝑎𝑛𝜃 =
2
√29
and cos
for the acute angle
in
.
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34. Use trigonometric identities to transform one side of the equation into the other.
𝜋
(0 < 𝜃 < 2 ).
𝑠𝑖𝑛𝜃𝑐𝑠𝑐𝜃 + tan2 𝜃 = sec 2 𝜃
35. Let (5, -12) be a point on the terminal side of an angle in standard position. Determine the
exact values of the six trigonometric functions of the angle.
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Long Answer Section [2 points each]
36. Consider the function
𝑥 2 −4
𝑓(𝑥 ) = 𝑥 2 −7𝑥+10. Find each of the following:
a. x-intercept
b. y-intercept
c. vertical and horizontal asymptote(s)
d. hole(s) if any
e. Carefully sketch the graph below. Label each feature from a-d
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Answer Key
1.
2. x = ±4
,h≠0
3.
4. All real numbers x such that x > 0
5. descreasing on (–∞, –1)
increasing on (–1, ∞)
6. Reflection in the x-axis; then vertical shift 5 units up.
7.
; all real numbers x except x =
8.
9. True
10. (8, 9)
11.
12.
13. Domain: all real numbers x except x = ±4
14.
15. x = –7
16.
17.
18.
19.
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20.
21.
22.
23.
24. 3rd quadrant
25.
26. Complement:
27. Supplement:
28. θ =
radians
29.
30.
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