AnswersPrecalculusTrigonometric Sum Identities

Trigonometric Sum Identities — Cumulative exam Answers

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21
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Which graph shows the solution set of ?

Question illustration
A
mc017-2.jpg
Option A
B
mc017-3.jpg
Option B
C
mc017-4.jpg
Option C
D
mc017-5.jpg
Option D
22
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What is written as a single logarithm?

Question illustration
A
4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed
Option A
B
log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)
Option B
C
log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)
Option C
D
log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4
Option D
23

If the interval (a, ∞) describes all values of x for which the graph of is decreasing, what is the value of a?

Answer not available
24

A waterwheel has a radius of 5 feet. The center of the wheel is 2 feet above the waterline. You notice a white mark at the top of the wheel. How many radians would the wheel have to rotate for the white mark to be 3 feet below the waterline?

A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
25

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–2, –1, 0, 2
B
–2, 0, 1, 2
C
–1, 0
D
0, 1
26

What function is graphed below?

Question illustration
A
mc019-2.jpg
Option A
B
mc019-3.jpg
Option B
C
mc019-4.jpg
Option C
D
mc019-5.jpg
Option D
27

Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?

A
f(x) =
Option A
B
f(x) =
Option B
C
f(x) =
Option C
D
f(x) =
Option D
28

Which of the pairs of functions and their inverses will always have a domain and range of all real numbers?

A
a pair of linear functions with defined slopes
B
a cubic function and a cube root function
C
a quadratic function and a square root function
D
a logarithmic function and an exponential function
29

Which graph shows the solution set of ?

Question illustration
A
mc019-2.jpg
Option A
B
mc019-3.jpg
Option B
C
mc019-4.jpg
Option C
D
mc019-5.jpg
Option D
30

Functions f(x) and g(x) are composed to form . If , what is the value of a?

Question illustration
A
0
B
–1
C
–2
D
–4
31

At which x-value does the cosine function attain a maximum value?

A
x = 0
B
x = StartFraction pi Over 2 EndFraction
Option B
C
x = 1
D
x = StartFraction 3 pi Over 2 EndFraction
Option D
32

Which graph represents the following piecewise defined function?

Question illustration
A
mc004-2.jpg
Option A
B
mc004-3.jpg
Option B
C
mc004-4.jpg
Option C
D
mc004-5.jpg
Option D
33

What is 4cos2(165°) – 2 expressed as a single trigonometric function?

A
4cos(330°)
B
2cos(330°)
C
4cos(82.5°)
D
2cos(82.5°)
34

Review the graph.

Question illustration
A
The period of the graph is
Option A
B
The amplitude of the graph is 2 units.
C
The domain of the graph is the set of x-values from –3 to 3, inclusive.
D
The graph represents a reflection over the x-axis of the function y = 3sin(2x).
35

Which step is included in the graph of the function ?

Question illustration
A
mc019-2.jpg
Option A
B
mc019-3.jpg
Option B
C
mc019-4.jpg
Option C
D
mc019-5.jpg
Option D
36

What are all the exact solutions of for ? Give your answer in radians.

Question illustration
A
mc017-3.jpg
Option A
B
and
Option B
C
and
Option C
D
, and
Option D
38

What is written as a single logarithm?

Question illustration
A
log Subscript 2 Baseline left-bracket StartFraction x cubed Over (StartFraction 3 Over x + 4 EndFraction) EndFraction Right-bracket
Option A
B
log Subscript 2 Baseline (StartFraction 3 x cubed Over x + 4 EndFraction)
Option B
C
log Subscript 2 Baseline left-bracket (StartStartFraction x cubed Over 3 EndFraction) Over x + 4 EndEndFraction Right-bracket
Option C
D
log Subscript 2 Baseline (StartFraction x cubed Over 3 + (x + 4) EndFraction)
Option D
39

Ingrid claims that . Review Ingrid’s steps in verifying her claim.Which statement describes Ingrid’s claim that and her steps in verifying her claim?

Question illustration
A
Ingrid’s claim is correct, and her steps are correct.
B
Ingrid’s claim is correct, but her steps are incorrect.
C
Ingrid’s claim is incorrect, but her steps are correct.
D
Ingrid’s claim is incorrect, and her steps are incorrect.
40

Which of the following accurately lists all of the discontinuities for the function graphed below?

Question illustration
A
jump discontinuity at x = 0; point discontinuity at x = 8
B
jump discontinuity at x = 0; point discontinuities at x = –2 and x = 8
C
jump discontinuities at x = 0 and x = 8; point discontinuity at x = –2
D
jump discontinuity at x = 0; point discontinuities at x = –2, x = 3 and x = 8
41

Amanda has a job that pays $35 per hour for the first 40 hours worked each week, plus 1.5 times this hourly rate for work done over 40 hours. Suppose Amanda works 50 hours this week. How much will she earn before taxes?

A
$1,575
B
$1,750
C
$1,925
D
$2,625

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