AnswersGA-GSE Pre-CalculusInverse of a Function

General Form of Sine and Cosine Answers

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A weight hangs from a spring attached to a ceiling, and the weight moves up and down. The table shows the distance in centimeters, y, between the weight and the ceiling after x seconds.

Question illustration
A
y = 7 sine (pi x) + 19
Option A
B
y = 7 sine (2 pi x) + 19
Option B
C
y = 3.5 sine (pi x) + 19
Option C
D
y = 3.5 sine (2 pi x) + 19)
Option D
2
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A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y = , where x is time in minutes.How many times does the fan rotate each minute?

Question illustration
A
1,000
B
2,000
C
4,000
D
6,000
3

The graph displays the function g(x) .

Question illustration
A
h (x) = 2 cosine (x minus StartFraction 3 pi Over 8 EndFraction) minus 1
Option A
B
h (x) = 2 cosine (x minus StartFraction 3 pi Over 8 EndFraction) minus 3
Option B
C
h (x) = 2 cosine (x + StartFraction 11 pi Over 8 EndFraction) minus 1
Option C
D
h (x) = 2 cosine (x + StartFraction 11 pi Over 8 EndFraction) minus 3
Option D
4

An object travels back and forth along a straight line. Its velocity, in centimeters per second, is given by the function v(t) = , where t is time in seconds.What is the maximum velocity of the object?

Question illustration
A
0 cm/s
B
13 cm/s
C
26 cm/s
D
90 cm/s
5

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a function has a maximum of 1 and minimum of negative 1. It completes one period at 2 pi. It crosses the y-axis at (0, 1).
Option A
B
On a coordinate plane, a function has a maximum of 0 and minimum of negative 2. It completes one period at 2 pi. It crosses the y-axis at (0, 0).
Option B
C
On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, 1).
Option C
D
On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, negative 3).
Option D
6

The water depth in a harbor rises and falls over time. The function f(t) = models the water depth, in feet, after t hours.During the first 24 hours, at what times does the water depth reach a maximum?

Question illustration
A
at 5 and 17 hours
B
at 11 and 23 hours
C
at 2, 8, 14, and 20 hours
D
at 5, 11, 17, and 23 hours
7

Consider the function . What transformation results in ?

Question illustration
A
translating 5 units down
B
translating 10 units down
C
reflecting across the x-axis
D
reflecting across the y-axis
8

Which graph represents the function after a shift of 3 units down?

Question illustration
A
On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at 4 pi. It increases through the y-axis at (0, negative 3).
Option A
B
On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at 4 pi. It crosses the y-axis at (0, negative 2).
Option B
C
On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at pi. It increases through the y-axis at (0, negative 3).
Option C
D
On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at pi. It crosses the y-axis at (0, negative 2).
Option D
9

The blades of a wind turbine are 135 feet long and are attached to the top of a 262-foot tower. The turbine completes 17 revolutions per minute. Suppose the tip of one of the blades starts at its maximum height above the ground.Which function represents the height, in feet, of the tip of this blade after t minutes?

A
f (t) = 270 cosine (17 pi t) + 262
Option A
B
f (t) = 135 cosine (17 pi t) + 262
Option B
C
f (t) = 270 cosine (34 pi t) + 262
Option C
D
f (t) = 135 cosine (34 pi t) + 262
Option D
10

Consider the graphs of and .Which feature of the graph of g(x) is different from the graph of f(x)?

Question illustration
A
the period
B
the amplitude
C
the phase shift
D
the vertical shift
11

A clock is positioned on an auditorium wall with its center 9 ft above the floor. The second hand on the clock is 10 inches long and continuously moves around the clock. Let x represent the time in seconds measured from noon on a given day.Which function f(x) represents the height above the floor, in feet, of the tip of the second hand?

A
f (x) = StartFraction 5 Over 6 EndFraction cosine (StartFraction pi Over 60 EndFraction x) + 9
Option A
B
f (x) = StartFraction 5 Over 6 EndFraction cosine (StartFraction pi Over 30 EndFraction x) + 9
Option B
C
f (x) = StartFraction 5 Over 6 EndFraction cosine (30 pi x) + 9
Option C
D
f (x) = StartFraction 5 Over 6 EndFraction cosine (120 pi x) + 9
Option D
12

The position of a paddle on a waterwheel after t seconds is modeled by f(t) = . A positive function value indicates the paddle is above the waterline, while a negative value indicates the paddle is below the waterline.What is the initial position of the paddle?

Question illustration
A
10.5 ft above the waterline
B
5.25 ft above the waterline
C
0 ft at the waterline
D
5.25 ft below the waterline
13

Suppose the function f(t) = models the height of a seat on a Ferris wheel after t minutes.Based on this information, what is the diameter of the Ferris wheel?

Question illustration
A
95 ft
B
120 ft
C
190 ft
D
215 ft
14

Which graph represents the function g(x) = 7cosx after a shift of units to the right?

Question illustration
A
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, 6).
Option A
B
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It decreases through the y-axis at (0, 4).
Option B
C
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, negative 6).
Option C
D
On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It increases through the y-axis at (0, 4).
Option D
15

The graph represents a function with the form f(x) = asin(bx + c).

Question illustration
A
a = 6, b = 1, c = StartFraction pi Over 3 EndFraction
Option A
B
a = 6, b = 3, c = pi
Option B
C
a = 3, b = 1, c = StartFraction pi Over 3 EndFraction
Option C
D
a = 3, b = 6, c = pi
Option D
16

Review the given functions.

Question illustration
A
a shift left units
Option A
B
a shift left units
Option B
C
a shift right units
Option C
D
a shift right units
Option D

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