AnswersAlgebra 2 SAT 26-27 Supplemental Wk3Inverse 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.

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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?

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

The graph displays the function g(x) .

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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?

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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

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