AnswersTX-Precalculus ACumulative Exam

Cumulative Exam — Cumulative exam Answers

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1
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What is the vertical shift of the graph of the parent cosecant function to the graph of the function below?

Question illustration
A
1 unit down
B
2 units down
C
3 units down
D
4 units down
2
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What is the value of ?

Question illustration
A
3
B
5
C
15
D
25
3

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
4

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
5

What is the approximate value of a local maximum for the polynomial?

Question illustration
A
–4.5
B
–2.5
C
0.5
D
2.5
6

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°)
7

The table shows several points for function j(t).

Question illustration
A
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries negative 1, negative 2, negative 10, negative 250.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 8, 10, 17.
Option D
8

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

Question illustration
A
1.5 days
B
2.5 days
C
9.4 days
D
21.1 days
9

Which trigonometric functions have a domain of [–1, 1]?

A
y = arcsinx and y = arccosx
B
y = arccosx and y = arctanx
C
y = arcsinx and y = arctanx
D
y = arcsecx and y = arccscx
10

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
11

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
12

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.
13

Consider the function f(x) = . What transformation results in g(x)?

Question illustration
A
Translate units left and 7 units up.
Option A
B
Translate units right and 7 units up.
Option B
C
Translate units left and 7 units down.
Option C
D
Translate units right and 7 units down.
Option D
14

A company’s equipment manager buys $7,000 worth of equipment. This equipment depreciates 19% each year. The manager can replace the equipment after its value falls below $500.After how many years can the manager first replace the equipment?

A
10
B
11
C
12
D
13
15

What is the exact value of cos(c + d), given for c in Quadrant II and for d in Quadrant III?

Question illustration
A
Negative StartFraction 47 Over 100 EndFraction
Option A
B
Negative 1 and StartFraction 3 Over 100 EndFraction
Option B
C
StartFraction 21 minus 24 StartRoot 7 EndRoot Over 100 EndFraction
Option C
D
StartFraction 21 + 24 StartRoot 7 EndRoot Over 100 EndFraction
Option D
16

The values in the table represent the graph of a continuous function. Which interval must contain an x-intercept?xy–3.1–1.85–2.7–0.84–2.3–0.09–1.90.44–1.50.79–1.11.00–0.71.10–0.31.130.11.13

A
–3.1 < x < –2.7
B
–2.3 < x < –1.9
C
–1.5 < x < –1.1
D
–0.3 < x < 0.1
17

Which is an x-intercept of the graph of the function ?

Question illustration
A
(StartFraction pi over 6 EndFraction, 0)
Option A
B
(StartFraction pi over 3 EndFraction , 0)
Option B
C
(3pi, 0)
Option C
D
(6pi, 0)
Option D
18

Suppose and sin(x) > 0. What is the value of tan(2x)?

Question illustration
A
Negative 5
Option A
B
Negative four-thirds
Option B
C
Four-thirds
Option C
D
2
19

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
20

Given the function g(x) = 41x3 + a for some constant a, which describes the inverse function g–1(x)?

A
no restriction on the domain of g(x); inverse is g–1(x) =
Option A
B
no restriction on the domain of g(x); inverse is g–1(x) =
Option B
C
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) =
Option C
D
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) =
Option D

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