AnswersAlgebra 2 MP 234 CHSChanges in Period and Phase Shift of Sine and Cosine Functions

Changes in Period and Phase Shift of Sine and Cosine Functions Answers

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Which of the following could be the equation of the function below?

Question illustration
A
y = negative 2 cosine (4 (x + pi)) minus 1
Option A
B
y = 2 cosine (x + pi) + 1
Option B
C
y = negative 2 cosine (2 (x + pi)) minus 1
Option C
D
y = 2 cosine (4 (x + pi)) + 2
Option D
2
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What is the general equation of a cosine function with an amplitude of 3, a period of , and a horizontal shift of ?

Question illustration
A
y = 4 pi cosine (3 (x minus pi))
Option A
B
y = 3 cosine (4 pi (x + pi))
Option B
C
y = 3 cosine (0.5 (x + pi))
Option C
D
y = 4 pi cosine (0.2 (x + pi))
Option D
3

Which transformations are needed to change the parent cosine function to ?

Question illustration
A
vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right
Option A
B
vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the left
Option B
C
vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the right
Option C
D
vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right
Option D
4

Which of the following is the graph of y = sin(0.5x)?

A
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 24 pi.
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 2 pi.
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 1 cycle at 8 pi.
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 8 pi.
Option D
5

Which term gives the number of cycles of a periodic function that occur in one horizontal unit?

A
vertical shift
B
period
C
frequency
D
phase shift
6

What is the equation of the graph below?

Question illustration
A
y = sine (StartFraction x Over 3 EndFraction)
Option A
B
y = sin(3x)
C
y = sin(0.3x)
D
y = sine (StartFraction 2 x Over 3 EndFraction)
Option D
7

Which transformations are needed to change the parent cosine function to ?

Question illustration
A
vertical compression of 3, horizontal stretch to a period of , phase shift of units to the left
Option A
B
vertical stretch of 3, horizontal compression to a period of , phase shift of units to the right
Option B
C
vertical compression of 3, horizontal stretch to a period of 10p, phase shift of units to the right
Option C
D
vertical stretch of 3, horizontal compression to a period of , phase shift of units to the left
Option D
8

What is the equation of the graph below?

Question illustration
A
y = cosine (x + StartFraction pi Over 2 EndFraction)
Option A
B
y = cosine (x + 2 pi)
Option B
C
y = cosine (x + StartFraction pi Over 3 EndFraction)
Option C
D
y = cosine (x + pi)
Option D
10

What is the phase shift of a periodic function?

A
a horizontal translation of the function
B
the horizontal length of one cycle of the function
C
the number of cycles of the function that occur in one horizontal unit
D
a vertical translation of the function

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