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 — Test Answers

25 verified answers
1
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Which is the graph of y = cos(x) + 3?

A
On a coordinate plane, a cosine curve has a maximum of 3 and a minimum of negative 3.
Option A
B
On a coordinate plane, a cosine curve has a maximum of 4 and a minimum of negative 2.
Option B
C
On a coordinate plane, a cosine curve has a maximum of negative 2 and a minimum of negative 4.
Option C
D
On a coordinate plane, a cosine curve has a maximum of 6 and a minimum of negative 0.
Option D
2
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Which function describes the graph below?

Question illustration
A
f (x) = 6 cosine (x)
Option A
B
f (x) = 3 cosine (x) + 3
Option B
C
f (x) = 6 sine (x)
Option C
D
f (x) = 3 sine (x) + 3
Option D
3

Which of the following is the graph of y = cos(2x)?

A
mc008-1.jpg
Option A
B
mc008-2.jpg
Option B
C
mc008-3.jpg
Option C
D
mc008-4.jpg
Option D
4

If angle B measures 25°, what is the approximate perimeter of the triangle below?

Question illustration
A
10.3 units
B
11.8 units
C
22.1 units
D
25.2 units
5

What is the length of x in the diagram below?

Question illustration
A
StartFraction 5 Over StartRoot 3 EndRoot
Option A
B
StartFraction 10 Over StartRoot 3 EndRoot EndFraction
Option B
C
5 StartRoot 3 EndRoot
Option C
D
10
6

What is the equation of the graph below?

Question illustration
A
y = sine (x + 90 degrees)
Option A
B
y = cosine (x + 90 degrees)
Option B
C
y = sine (x + 45 degrees)
Option C
D
y = cosine (x + 45 degrees)
Option D
7

In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypotenuse of the triangle?

A
3.4 centimeters
B
10.6 centimeters
C
27.5 centimeters
D
29.2 centimeters
8

Which function will have a y-intercept at –1 and an amplitude of 2?

A
f (x) = negative sine (X) minus 1
Option A
B
f (x) = negative 2 sine (x) minus 1
Option B
C
f (x) = negative cosine (x)
Option C
D
f (x) = negative 2 cosine (x) minus 1
Option D
9

The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?

A
ft
Option A
B
ft
Option B
C
ft
Option C
D
ft
Option D
10

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

Question illustration
A
y = negative 3 sine (2 (x + pi)) + 2
Option A
B
y = negative 3 sine (x + pi) + 2
Option B
C
y = 3 sine (4 (x minus pi)) + 4
Option C
D
y = 3 sine (2 (x + pi)) + 2
Option D
11

What is the range of y = –3sin(x) – 4?

A
all real numbers
Option A
B
all real numbers
Option B
C
all real numbers
Option C
D
all real numbers
Option D
12

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

Question illustration
A
y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2
Option A
B
y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2
Option B
C
y = 0.5 cosine (4 (x + pi)) + 2
Option C
D
y = 0.5 cosine (2 (x minus pi)) minus 2
Option D
13

Which function has the given properties below?The domain is the set of all real numbers.One x-intercept is .The amplitude is 4.The point is on the graph.The y-intercept is (0, 0).

Question illustration
A
y = –4sin(x)
B
y = –4cos(x)
C
y = 4sin(x)
D
y = 4cos(x)
14

Which function is graphed below?

Question illustration
A
f(x) = cos(x)
B
f(x) = –cos(x)
C
f(x) = sin(x)
D
f(x) = –sin(x)
15

The sides of which diagram are correctly labeled with respect to angle A?

A
A right triangle is shown. Angle A is opposite to the side labeled adjacent.
Option A
B
A right triangle is shown. Angle A is opposite to the side labeled opposite. The hypotenuse is opposite to the right angle.
Option B
C
A right triangle is shown. Angle A is opposite to the side labeled opposite. The side labeled adjacent is opposite to the right angle.
Option C
D
A right triangle is shown. Angle A is opposite to the side labeled hypotenuse. The side labeled adjacent is opposite to the right angle.
Option D
16

One leg of a right triangle measures 6 inches. The remaining leg measures inches. What is the measure of the angle opposite the leg that is 6 inches long?

Question illustration
A
30°
B
45°
C
60°
D
90°
17

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
18

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
19

What is the period of f(x) = sin(x)?

A
StartFraction pi Over 2 EndFraction
Option A
B
Pi
Option B
C
StartFraction 3 pi Over 2 EndFraction
Option C
D
2 pi
Option D
20

What is the amplitude of the function below?

Question illustration
A
1
B
2
C
Pi
Option C
D
2 pi
Option D

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