AnswersAlgebra 2 MP 234 CHSChanges in Period and Phase Shift of Sine and Cosine Functions

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

0 verified answers1 views
1
Free Preview

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
2
Free Preview

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

A
StartFraction pi Over 3 EndFraction
Option A
B
StartFraction 2 pi Over 3 EndFraction
Option B
C
3 pi
Option C
D
6 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 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
5

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
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

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

Question illustration
A
y = 4 pi cosine (3 (x minus pi))
Option A
B
y = 3 cosine (4 pi (x + pi))
Option B
C
y = 3 cosine (0.5 (x + pi))
Option C
D
y = 4 pi cosine (0.2 (x + pi))
Option D
8

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
9

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
10

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

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Changes in Period and Phase Shift of Sine and Cosine Functions

Quiz
10 verified answers

Absolute Value Functions

Quiz
10 verified answers

Changes in Period and Phase Shift of Sine and Cosine Functions