AnswersCommon Core Precalculus - MA3112 Quarter 1Linear and Angular Velocity

General Form of Sine and Cosine Answers

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1
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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
2
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Which graph represents the function ?

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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
3

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
4

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
5

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
6

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
7

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
8

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
9

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

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