Changes in Period and Phase Shift of Sine and Cosine Functions Answers
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1
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What is the period of y = sin(3x)?
A
StartFraction pi Over 3 EndFraction
B
StartFraction 2 pi Over 3 EndFraction
C
3 pi
D
6 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 ?
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))
3
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
4
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 function5
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
6
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.
7
Which of the following could be the equation of the function below?
A
y = negative 2 cosine (4 (x + pi)) minus 1
B
y = 2 cosine (x + pi) + 1
C
y = negative 2 cosine (2 (x + pi)) minus 1
D
y = 2 cosine (4 (x + pi)) + 2
8
What is the general equation of a sine function with an amplitude of 2, a period of and a horizontal shift of units?
A
y = 2 sine (2 (x minus pi))
B
y = 2 sine (4 (x + pi))
C
y = sine (0.5 (x minus pi))
D
y = sine (2 (x + pi))
9
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.
10
Which transformations are needed to change the parent cosine function to the cosine function below?
A
vertical stretch of 2, horizontal stretch to a period of , phase shift of units to the right, vertical shift of 1 unit up
B
vertical compression of 2, horizontal stretch to a period of , phase shift of units to the left, vertical shift of 2 units down
C
vertical compression of 2, horizontal compression to a period of , phase shift of units to the left, vertical shift of 1 unit down
D
vertical stretch of 2, horizontal compression to a period of , phase shift of units to the right, vertical shift of 1 unit down
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