Changes in Period and Phase Shift of Sine and…

Which of the following is the graph of y is equal to cosine of open paren 2 times open paren x plus pi close paren close paren ?

A

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 7 pi comma 1). It starts to fall through (negative 6 pi comma 0) to (negative 5 pi comma negative 1). It then rises through (negative 4 pi comma 0) to (negative 3 pi comma 1). It then falls through (negative 2 pi comma 0) to (negative pi comma negative 1). It then rises through (0 comma 0) to (pi comma 1). It then falls through (2 pi comma 0) to (3 pi comma negative 1). It then rises though (4 pi comma 0) to (5 pi comma 1). It then falls through (6 pi comma 0) to (7 pi comma negative 1). It then rises through (8 pi comma 0).

B

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 6 pi comma 1). It starts to fall through (negative 4 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (0 comma 0) to (2 pi comma 1). It then falls through (4 pi comma 0) to (6 pi comma negative 1). It then rises through (8 pi comma 0).

C

Image with description A coordinate plane. The graph starts and rises through (negative 2 pi comma 0) to (negative 7 pi over 4 comma 1). It starts to fall through (negative 3 pi over 2 comma 0) to (negative 5 pi over 4 comma negative 1). It then rises through (negative pi comma 0) to (negative 3 pi over 4 comma 1). It then falls through (negative pi over 2 comma 0) to (negative pi over 4 comma negative 1). It then rises through (0 comma 0) to (pi over 4 comma 1). It then falls through (pi over 2 comma 0) to (3 pi over 4 comma negative 1). It then rises though (pi comma 0) to (5 pi over 4 comma 1). It then falls through (3 pi over 2 comma 0) to (7 pi over 4 comma negative 1). It then rises through (2 pi comma 0).

D

Image with description A coordinate plane. The graph starts and rises through (negative 24 pi comma 0) to (negative 21 pi comma 1). It starts to fall through (negative 18 pi comma 0) to (negative 15 pi comma negative 1). It then rises through (negative 12 pi comma 0) to (negative 9 pi comma 1). It then falls through (negative 6 pi comma 0) to (negative 3 pi comma negative 1). It then rises through (0 comma 0) to (3 pi comma 1). It then falls through (6 pi comma 0) to (9 pi comma negative 1). It then rises though (12 pi comma 0) to (15 pi comma 1). It then falls through (18 pi comma 0) to (21 pi comma negative 1). It then rises through (24 pi comma 0).

2

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Which of the following is the graph of y is equal to sine of 0 point 5 x ?

A

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 6 pi comma 1). It then falls through (negative 4 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (0 comma 0) to (2 pi comma 1). It then falls through (4 pi comma 0) to (6 pi comma negative 1). It then rises through (8 pi comma 0).

B

Image with description A coordinate plane. The graph starts and falls through (negtiave pi comma 2) to (negative 3 pi over 4 comma negative 1). It rises through (negtiave pi over 2 comma 2) to (negative pi over 4 comma 5). It then falls through (0 comma 2) to (pi over 4 comma negative 1). It then rises through (pi comma 2) to (3 pi over 4 comma 5).

C

Image with description A coordinate plane. The graph starts and rises to (negative pi comma negative 1.5). It then falls through (negative 7 pi over 8 comma negative 2) to (negative 3 pi over 4 comma negative 2.5). It then rises through (negative 5 pi over 8 comma negative 2) to (negative pi over 2 comma negative 1.5). It then falls through (negative 3 pi over 8 comma negative 2) to (negative pi over 4 comma negative 2.5). It then rises through (negative pi over 8 comma negative 2) to (0 comma negative 1.5). It then falls through (pi over 8 comma negative 2) to (negative pi over 4 comma negative 2.5). It then rises through (3 pi over 8 comma negative 2) to (pi over 2 comma negative 1.5). It then falls through (5 pi over 8 comma negative 2) to (3 pi over 4 comma negative 2.5). It then rises through (7 pi over 8 comma negative 2) to (pi comma negative 1.5).

D

Image with description A coordinate plane. The graph starts and rises to (negative 360 comma 1). It starts to fall through (negative 270 comma 0) to (negative 180 comma negative 1). It then rises through (negative 90 comma 0) to (0 comma 1). It then falls through (90 comma 0) to (180 comma negative 1). It then rises through (270 comma 0) to (360 comma 1).

3

The graph of y is equal to cosine of open paren x plus pi over 2 close paren is the graph of the y is equal to cosine of x shifted in which direction?

A

pi over 2 units up

B

pi over 2 units down

C

pi over 2 units to the left

D

pi over 2 units to the right

4

What is the general equation of a cosine function with an amplitude of 3 , a period of 4 pi , and a horizontal shift of negative pi ?

A

y is equal to 3 cosine open paren 4 pi open paren x plus pi close paren close paren

B

y is equal to 3 cosine open paren 0 point 5 times open paren x plus pi close paren close paren

C

y is equal to 4 pi cosine open paren 3 times open paren x minus pi close paren close paren

D

y is equal to 4 pi cosine open paren 0 point 2 times open paren x plus pi close paren close paren

5

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

A

period

B

frequency

C

phase shift

D

vertical shift

6

What is the phase shift of a periodic function ?

A

a horizontal translation of the function

B

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

C

the horizontal length of one cycle of the function

D

a vertical translation of the function

7

What is the period of y is equal to sine of 3 x ?

A

3 pi

B

2 pi over 3

C

6 pi

D

pi over 3

8

The graph of y is equal to sine of open paren x minus 3 pi over 2 close paren is the graph of the y is equal to sine of x shifted in which direction?

A

3 pi over 2 units down

B

3 pi over 2 units to the left

C

3 pi over 2 units to the right

D

3 pi over 2 units up

9

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

A

frequency

B

phase shift

C

amplitude

D

period

10

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

A

y is equal to sine of open paren 2 times open paren x plus pi close paren close paren

B

y is equal to 2 sine open paren 2 times open paren x minus pi close paren close paren

C

y is equal to sine of open paren 0 point 5 times open paren x minus pi close paren close paren

D

y is equal to 2 sine open paren 4 times open paren x plus pi close paren close paren

11

The graph of y is equal to cosine of open paren x plus pi over 2 close paren is the graph of the y is equal to cosine of x shifted in which direction?

A

pi over 2 units to the left

B

pi over 2 units down

C

pi over 2 units up

D

pi over 2 units to the right

12

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

A

y is equal to 2 sine open paren 4 times open paren x plus pi close paren close paren

B

y is equal to sine of open paren 0 point 5 times open paren x minus pi close paren close paren

C

y is equal to sine of open paren 2 times open paren x plus pi close paren close paren

D

y is equal to 2 sine open paren 2 times open paren x minus pi close paren close paren

13

The graph of y is equal to sine of open paren x minus 3 pi over 2 close paren is the graph of the y is equal to sine of x shifted in which direction?

A

3 pi over 2 units to the left

B

3 pi over 2 units up

C

3 pi over 2 units down

D

3 pi over 2 units to the right

14

What is the period of y is equal to sine of 3 x ?

A

3 pi

B

6 pi

C

pi over 3

D

2 pi over 3

15

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

A

period

B

vertical shift

C

phase shift

D

frequency

16

What is the phase shift of a periodic function ?

A

the horizontal length of one cycle of the function

B

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

C

a vertical translation of the function

D

a horizontal translation of the function

17

Which of the following is the graph of y is equal to sine of 0 point 5 x ?

A

Image with description A coordinate plane. The graph starts and rises to (negative 360 comma 1). It starts to fall through (negative 270 comma 0) to (negative 180 comma negative 1). It then rises through (negative 90 comma 0) to (0 comma 1). It then falls through (90 comma 0) to (180 comma negative 1). It then rises through (270 comma 0) to (360 comma 1).

B

Image with description A coordinate plane. The graph starts and falls through (negtiave pi comma 2) to (negative 3 pi over 4 comma negative 1). It rises through (negtiave pi over 2 comma 2) to (negative pi over 4 comma 5). It then falls through (0 comma 2) to (pi over 4 comma negative 1). It then rises through (pi comma 2) to (3 pi over 4 comma 5).

C

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 6 pi comma 1). It then falls through (negative 4 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (0 comma 0) to (2 pi comma 1). It then falls through (4 pi comma 0) to (6 pi comma negative 1). It then rises through (8 pi comma 0).

D

Image with description A coordinate plane. The graph starts and rises to (negative pi comma negative 1.5). It then falls through (negative 7 pi over 8 comma negative 2) to (negative 3 pi over 4 comma negative 2.5). It then rises through (negative 5 pi over 8 comma negative 2) to (negative pi over 2 comma negative 1.5). It then falls through (negative 3 pi over 8 comma negative 2) to (negative pi over 4 comma negative 2.5). It then rises through (negative pi over 8 comma negative 2) to (0 comma negative 1.5). It then falls through (pi over 8 comma negative 2) to (negative pi over 4 comma negative 2.5). It then rises through (3 pi over 8 comma negative 2) to (pi over 2 comma negative 1.5). It then falls through (5 pi over 8 comma negative 2) to (3 pi over 4 comma negative 2.5). It then rises through (7 pi over 8 comma negative 2) to (pi comma negative 1.5).

18

Which of the following is the graph of y is equal to cosine of open paren 2 times open paren x plus pi close paren close paren ?

A

Image with description A coordinate plane. The graph starts and rises through (negative 2 pi comma 0) to (negative 7 pi over 4 comma 1). It starts to fall through (negative 3 pi over 2 comma 0) to (negative 5 pi over 4 comma negative 1). It then rises through (negative pi comma 0) to (negative 3 pi over 4 comma 1). It then falls through (negative pi over 2 comma 0) to (negative pi over 4 comma negative 1). It then rises through (0 comma 0) to (pi over 4 comma 1). It then falls through (pi over 2 comma 0) to (3 pi over 4 comma negative 1). It then rises though (pi comma 0) to (5 pi over 4 comma 1). It then falls through (3 pi over 2 comma 0) to (7 pi over 4 comma negative 1). It then rises through (2 pi comma 0).

B

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 7 pi comma 1). It starts to fall through (negative 6 pi comma 0) to (negative 5 pi comma negative 1). It then rises through (negative 4 pi comma 0) to (negative 3 pi comma 1). It then falls through (negative 2 pi comma 0) to (negative pi comma negative 1). It then rises through (0 comma 0) to (pi comma 1). It then falls through (2 pi comma 0) to (3 pi comma negative 1). It then rises though (4 pi comma 0) to (5 pi comma 1). It then falls through (6 pi comma 0) to (7 pi comma negative 1). It then rises through (8 pi comma 0).

C

Image with description A coordinate plane. The graph starts and rises through (negative 8 pi comma 0) to (negative 6 pi comma 1). It starts to fall through (negative 4 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (0 comma 0) to (2 pi comma 1). It then falls through (4 pi comma 0) to (6 pi comma negative 1). It then rises through (8 pi comma 0).

D

Image with description A coordinate plane. The graph starts and rises through (negative 24 pi comma 0) to (negative 21 pi comma 1). It starts to fall through (negative 18 pi comma 0) to (negative 15 pi comma negative 1). It then rises through (negative 12 pi comma 0) to (negative 9 pi comma 1). It then falls through (negative 6 pi comma 0) to (negative 3 pi comma negative 1). It then rises through (0 comma 0) to (3 pi comma 1). It then falls through (6 pi comma 0) to (9 pi comma negative 1). It then rises though (12 pi comma 0) to (15 pi comma 1). It then falls through (18 pi comma 0) to (21 pi comma negative 1). It then rises through (24 pi comma 0).

19

What is the general equation of a cosine function with an amplitude of 3 , a period of 4 pi , and a horizontal shift of negative pi ?

A

y is equal to 4 pi cosine open paren 0 point 2 times open paren x plus pi close paren close paren

B

y is equal to 3 cosine open paren 0 point 5 times open paren x plus pi close paren close paren

C

y is equal to 3 cosine open paren 4 pi open paren x plus pi close paren close paren

D

y is equal to 4 pi cosine open paren 3 times open paren x minus pi close paren close paren

20

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

A

amplitude

B

period

C

phase shift

D

frequency

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

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