AnswersTX-Precalculus AUnit Test

Unit Test — Unit test Answers

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Consider the function y = cos(x). Which change would increase the period by a factor of 3?

A
Multiply cos(x) by
Option A
B
Multiply cos(x) by 3.
C
Multiply x by
Option C
D
Multiply x by 3.
2
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Which of the following is the equation of the function below?

Question illustration
A
y equal to 2 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.
Option A
B
y equal to 2 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) minus 1 right-square-bracket.
Option B
C
y equal to 0 point 5 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.
Option C
D
y equal to 0 point 5 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) right-square-bracket minus 1.
Option D
3

How many degrees is radians?

Question illustration
A
84.375°
B
93.75°
C
168.75°
D
337.5°
4

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures are shown.

Question illustration
A
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option A
B
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option B
C
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option C
D
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option D
5

Which transformation should be applied to the graph of the function to obtain the graph of the function ?

Question illustration
A
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option A
B
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option B
C
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option C
D
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option D
6

What is the equation of the graph below?

Question illustration
A
y = sec(x) + 2
B
y = csc(x) + 2
C
y = csc(x + 2)
D
y = sec(x + 2)
7

Review the graph.

Question illustration
A
y = tanx
B
y = cosx
C
y = tan-1x
D
y = cos-1x
8

What is the period of the function ?

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
9

Which expression is equivalent to 30°?

A
Inverse of cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
Inverse of sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option B
C
Sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
Cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
10

During high tide around 11:00 p.m., the water level is 3 feet above a marker on a pier. The following day, during low tide around 5:12 a.m., the water level has dropped 3 feet below the marker. The height of the water is modeled by the function , where x is the time in hours since 11:00 p.m.What is the height of the water at 2:15 a.m.?

Question illustration
A
0.22 feet below the marker
B
0.07 feet below the marker
C
1.26 feet above the marker
D
1.39 feet above the marker
11

The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are in their seats. What is the linear velocity of the children in feet per hour?

A
360π
B
720π
C
21,600π
D
43,200π
13

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 200 feet. Suppose the wheel rotates 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation?

A
50 feet
B
feet
Option B
C
100 feet
D
feet
Option D
14

Suppose the function h(x) = sinx is translated units left and 11 units down. Which graph represents the result?

Question illustration
A
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).
Option A
B
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).
Option B
C
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).
Option C
D
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).
Option D
15

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

Question illustration
A
(minus StartFraction 2pi over 3 EndFraction , 0)
Option A
B
(minus StartFraction pi over 3 EndFraction , 0)
Option B
C
(StartFraction pi over 6 EndFraction , 0)
Option C
D
(StartFraction 5pi over 6 EndFraction , 0)
Option D
16

Review the graph.

Question illustration
A
y = –3cos(x)
B
y = –3sin(x)
C
y = 3cos(x)
D
y = 3sin(x)
17

Over which interval is the graph of y = cos(x) strictly increasing?

A
0 less-than x less-than StartFraction pi Over 2 EndFraction
Option A
B
0 < x < π
C
StartFraction pi Over 2 EndFraction less-than x less-than StartFraction 3 pi Over 2 EndFraction
Option C
D
π < x < 2π
18

Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?

A
–2
B
Negative one-half
Option B
C
One-half
Option C
D
2
19

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Question illustration
A
Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.
Option A
B
Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.
Option B
C
Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.
Option C
D
Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.
Option D
20

At a certain location, the number of hours of sunlight is modeled by y = where x represents the number of weeks after the summer solstice.Based on the model, what is the minimum number of hours of sunlight at this location?

Question illustration
A
3.2
B
5.6
C
6.4
D
13.0
21

In which quadrant(s) is csc(x) positive?

A
quadrant I only
B
quadrant II only
C
quadrants I and II
D
quadrants I and III

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