Answers AZ-Common Core Algebra II BChanges 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?

y = negative 2 cosine (4 (x + pi)) minus 1

y = 2 cosine (x + pi) + 1

y = negative 2 cosine (2 (x + pi)) minus 1

y = 2 cosine (4 (x + pi)) + 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 ?

y = 4 pi cosine (3 (x minus pi))

y = 3 cosine (4 pi (x + pi))

y = 3 cosine (0.5 (x + pi))

y = 4 pi cosine (0.2 (x + pi))

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

vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right

vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the left

vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the right

vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right

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

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.

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.

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.

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.

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

vertical shift

period

frequency

phase shift

What is the equation of the graph below?

y = sine (StartFraction x Over 3 EndFraction)

y = sin(3x)

y = sin(0.3x)

y = sine (StartFraction 2 x Over 3 EndFraction)

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

vertical compression of 3, horizontal stretch to a period of , phase shift of units to the left

vertical stretch of 3, horizontal compression to a period of , phase shift of units to the right

vertical compression of 3, horizontal stretch to a period of 10p, phase shift of units to the right

vertical stretch of 3, horizontal compression to a period of , phase shift of units to the left

What is the equation of the graph below?

y = cosine (x + StartFraction pi Over 2 EndFraction)

y = cosine (x + 2 pi)

y = cosine (x + StartFraction pi Over 3 EndFraction)

y = cosine (x + pi)

What is the phase shift of a periodic function?

a horizontal translation of the function

the horizontal length of one cycle of the function

the number of cycles of the function that occur in one horizontal unit

a vertical translation of the function

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

vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right

vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the left

vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the right

vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right

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

vertical shift

period

frequency

phase shift

The graph of is the graph of the y = cos(x) shifted in which direction?

units to the left

units to the right

units up

units down

What is the general equation of a cosine function with an amplitude of 3, a period of , and a horizontal shift of ?

y = 4 pi cosine (3 (x minus pi))

y = 3 cosine (4 pi (x + pi))

y = 3 cosine (0.5 (x + pi))

y = 4 pi cosine (0.2 (x + pi))

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

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.

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.

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.

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.

What is the period of y = sin(3x)?

StartFraction pi Over 3 EndFraction

StartFraction 2 pi Over 3 EndFraction

3 pi

6 pi

Which term gives the horizontal length of one cycle of a periodic function?

amplitude

period

frequency

phase shift

Which of the following is the graph of ?

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.

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.