AnswersGA-GSE Pre-CalculusInverse of a Function

Inverse of a Function — Unit test Answers

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21
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The average daily high temperature in Madrid peaks at 92°F in the summer and drops as low as 33°F in the winter. The temperature can be modeled by , where d represents the day number of the year (January 1 is 1, January 2 is 2, and so on). During which day is the high temperature expected to be closest to 75°F?

Question illustration
A
106
B
63
C
270
D
204
22
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Review the graph.

Question illustration
A
y = sinx
B
y = cosx
C
y = arcsinx
D
y = arccosx
23

Review the graph.

Question illustration
A
y = sinx
B
y = cosx
C
y = arcsinx
D
y = arccosx
24

The water level in a harbor is described by the function , where y represents the water level measured in feet, and x represents the number of hours since high tide. The period of time between high tides is 12 hours. After approximately how many hours is the water expected to reach a depth of 28 feet the second time? Round to the nearest hour.

Question illustration
A
1 hour
B
2 hours
C
10 hours
D
12 hours
25

Which is the graph of the function ?

Question illustration
A
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 2. The curve crosses the x axis at (pi comma 0), (0 comma 0) and (negative pi comma 0).
Option A
B
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 2. The curve crosses the x axis at (pi comma 0), (0 comma 0) and (negative pi comma 0).
Option B
C
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 4. The curve crosses the x axis at (pi by 2 comma 0) and (negative 3 pi by 4 comma 0). The y-intercept is at (0 comma negative 2).
Option C
D
On a coordinate plane, the x axis ranges from negative pi to pi with an interval of pi by 4 units and the y axis ranges from negative 6 to 6 with an interval of 2 units. It shows a curve that oscillates between positive and negative infinity as x approaches multiples of pi. The curve has vertical asymptotes at x equals plus or minus n times pi by 4. The curve crosses the x axis at (pi by 2 comma 0) and (negative 3 pi by 4 comma 0). The y-intercept is at (0 comma negative 1).
Option D
26

Which statement is true about y = arctanx?

A
The domain is .
Option A
B
The range is all real numbers.
C
The graph contains vertical asymptotes.
D
The graph is symmetric about the origin.
27

Annabelle’s bicycle has a wheel radius of 13 inches. She places a sticker on the wheel so that its minimum height above the ground is 0.5 inches. When she rides her bicycle, the wheel completes 90 revolutions every minute. The sticker begins at its minimum height above the ground.Which equation models the height in inches of the sticker after x minutes?

A
y = 0.5 sine (180 pi x) + 13
Option A
B
y = 12.5 sine (180 pi x) + 13
Option B
C
y = 0.5 sine (180 pi x minus StartFraction pi Over 2 EndFraction) + 13
Option C
D
y = 12.5 sine (180 pi x minus StartFraction pi over 2 EndFraction) + 13
Option D
28

Which is equal to –214°?

A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
29

What is the domain of y = cos-1x?

A
[–1, 1]
B
[0, π]
C
Left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option C
D
(–∞, ∞)
30

For what value of θ is ?

Question illustration
A
StartFraction pi Over 6 EndFraction
Option A
B
StartFraction pi Over 4 EndFraction
Option B
C
StartFraction pi Over 3 EndFraction
Option C
D
StartFraction pi Over 2 EndFraction
Option D
31

What is the range of y = sin-1x?

A
[–1, 1]
B
[0, π]
C
Left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option C
D
(–∞, ∞)
32

The function models the average high temperature in degrees Fahrenheit each month throughout the year in Anchorage, Alaska, where m = 1 for January and m = 12 for December. Approximately how many months is the average high temperature above freezing (32°F)?

Question illustration
A
7
B
11
C
10
D
8
33

The time it takes a spinner to stop completely is 12 seconds. If the spinner completes 6 revolutions in this time, what was the average angular velocity of the spinner, in radians per second, for the 12-second interval?

A
π
B
2π
C
4π
D
12π
34

Which of the following is the equation of the function below?

Question illustration
A
y equal to 2 secant (x plus StartFraction pi over 6 EndFraction) plus 2.
Option A
B
y equal to 2 secant left-square-bracket 2 (x plus StartFraction pi over 6 EndFraction) plus 2.
Option B
C
y equal to 2 secant left-square-bracket 2 (x minus 2) plus StartFraction pi over 6 EndFraction.
Option C
D
y equal to 2 secant (x plus 2) plus StartFraction pi over 6 EndFraction.
Option D
35

Which graph represents the function y = cos(4x)?

A
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 1).
Option A
B
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 1).
Option B
C
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 0).
Option C
D
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 0).
Option D
36

The water level at a pier is modeled by the function , where y represents the water level measured in meters, and x represents the number of hours since the last high tide. After how many hours is the water first expected to reach a depth of 12 meters? Round to the nearest tenth of an hour.

Question illustration
A
1.6 hours
B
3.1 hours
C
14.4 hours
D
19.6 hours
37

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
38

Earth revolves on its axis once every 24 hours. Which statements are true? Check all that apply.The angular velocity of Earth is π/12 radians per hour. The angular velocity of Earth is π/12 radians per day. The angular velocity of Earth is 2π radians per hour.The angular velocity of Earth is 2π radians per day. The angular velocity of Earth is 12π radians per day.

A
The angular velocity of Earth is π/12 radians per hour.
B
The angular velocity of Earth is π/12 radians per day.
C
The angular velocity of Earth is 2π radians per hour.
D
The angular velocity of Earth is 2π radians per day.
E
The angular velocity of Earth is 12π radians per day.
39

Review the graph.

Question illustration
A
On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 3, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 1.
Option A
B
On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 2, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 4.
Option B
C
On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 4, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 2.
Option C
D
On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 3, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 1.
Option D
40

What is the value of cos(tan-1(0))?

A
–1
B
0
C
1
D
StartFraction pi Over 2 EndFraction
Option D

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