Changes in Period and Phase Shift of Sine and Cosine Functions Answers
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1
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The graph of is the graph of the y = sin(x) shifted in which direction?
A
units to the left
B
units to the right
C
units up
D
units down
2
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What is the phase shift of a periodic function?
A
a horizontal translation of the functionB
the horizontal length of one cycle of the functionC
the number of cycles of the function that occur in one horizontal unitD
a vertical translation of the function3
What is the equation of the graph below?
A
y = cosine (x + StartFraction pi Over 2 EndFraction)
B
y = cosine (x + 2 pi)
C
y = cosine (x + StartFraction pi Over 3 EndFraction)
D
y = cosine (x + pi)
4
Which transformations are needed to change the parent cosine function to ?
A
vertical compression of 3, horizontal stretch to a period of , phase shift of units to the left
B
vertical stretch of 3, horizontal compression to a period of , phase shift of units to the right
C
vertical compression of 3, horizontal stretch to a period of 10p, phase shift of units to the right
D
vertical stretch of 3, horizontal compression to a period of , phase shift of units to the left
5
Which of the following is the graph of ?
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.
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.
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.
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.
6
Which transformations are needed to change the parent cosine function to ?
A
vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right
B
vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the left
C
vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the right
D
vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right
7
Which term gives the number of cycles of a periodic function that occur in one horizontal unit?
A
vertical shiftB
periodC
frequencyD
phase shift8
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.
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.
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.
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.
9
The graph of is the graph of the y = cos(x) shifted in which direction?
A
units to the left
B
units to the right
C
units up
D
units down
10
What is the general equation of a cosine function with an amplitude of 3, a period of , and a horizontal shift of ?
A
y = 4 pi cosine (3 (x minus pi))
B
y = 3 cosine (4 pi (x + pi))
C
y = 3 cosine (0.5 (x + pi))
D
y = 4 pi cosine (0.2 (x + pi))
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