AnswersAZ-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

14 verified answers3 views
1
Free Preview

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

Question illustration
A
units to the left
Option A
B
units to the right
Option B
C
units up
Option C
D
units down
Option D
2
Free Preview

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.
Option A
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.
Option B
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.
Option C
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.
Option D
3

What is the equation of the graph below?

Question illustration
A
y = sine (StartFraction x Over 3 EndFraction)
Option A
B
y = sin(3x)
C
y = sin(0.3x)
D
y = sine (StartFraction 2 x Over 3 EndFraction)
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
5

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

Question illustration
A
vertical compression of 3, horizontal stretch to a period of , phase shift of units to the left
Option A
B
vertical stretch of 3, horizontal compression to a period of , phase shift of units to the right
Option B
C
vertical compression of 3, horizontal stretch to a period of 10p, phase shift of units to the right
Option C
D
vertical stretch of 3, horizontal compression to a period of , phase shift of units to the left
Option D
6

Which of the following could be the equation of the function below?

Question illustration
A
y = negative 2 cosine (4 (x + pi)) minus 1
Option A
B
y = 2 cosine (x + pi) + 1
Option B
C
y = negative 2 cosine (2 (x + pi)) minus 1
Option C
D
y = 2 cosine (4 (x + pi)) + 2
Option D
7

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
8

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

A
amplitude
B
period
C
frequency
D
phase shift
9

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
10

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

Question illustration
A
vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right
Option A
B
vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the left
Option B
C
vertical compression of 0.35, horizontal compression to a period of , phase shift of units to the right
Option C
D
vertical stretch of 0.35, horizontal stretch to a period of , phase shift of units to the right
Option D
11

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

Question illustration
A
units to the left
Option A
B
units to the right
Option B
C
units up
Option C
D
units down
Option D
12

What is the equation of the graph below?

Question illustration
A
y = cosine (x + StartFraction pi Over 2 EndFraction)
Option A
B
y = cosine (x + 2 pi)
Option B
C
y = cosine (x + StartFraction pi Over 3 EndFraction)
Option C
D
y = cosine (x + pi)
Option D
13

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

A
vertical shift
B
period
C
frequency
D
phase shift
14

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

Did you find these answers helpful?

More from this Course

Quiz
15 verified answers

Law of Sines and Law of Cosines — a Deeper Look

Quiz
10 verified answers

Changes in Period and Phase Shift of Sine and Cosine Functions

Quiz
10 verified answers

Absolute Value Functions