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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1
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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
2
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What is the general equation of a sine function with an amplitude of 2, a period of and a horizontal shift of units?

Question illustration
A
y = 2 sine (2 (x minus pi))
Option A
B
y = 2 sine (4 (x + pi))
Option B
C
y = sine (0.5 (x minus pi))
Option C
D
y = sine (2 (x + pi))
Option D
3

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, negative 1). It has a minimum of negative 1 and a maximum of 1. It goes through 2 cycles at pi.
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, negative 1). It has a minimum of negative 1 and a maximum of 1. It goes through 1 cycle at pi.
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a minimum of negative 1 and a maximum of 1. It goes through 1 cycle at 4 pi.
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a minimum of negative 1 and a maximum of 1. It goes through 2 cycles at 2 pi.
Option D
4

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

Question illustration
A
vertical stretch of 2, horizontal stretch to a period of , phase shift of units to the right, vertical shift of 1 unit up
Option A
B
vertical compression of 2, horizontal stretch to a period of , phase shift of units to the left, vertical shift of 2 units down
Option B
C
vertical compression of 2, horizontal compression to a period of , phase shift of units to the left, vertical shift of 1 unit down
Option C
D
vertical stretch of 2, horizontal compression to a period of , phase shift of units to the right, vertical shift of 1 unit down
Option D

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