AnswersAZ-Common Core Algebra II BGraphing Sine and Cosine

Graphing Sine and Cosine Answers

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1
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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)
2
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Which set of transformations is needed to graph f(x) = –2sin(x) + 3 from the parent sine function?

A
vertical compression by a factor of 2, vertical translation 3 units up, reflection across the y-axis
B
vertical compression by a factor of 2, vertical translation 3 units down, reflection across the x-axis
C
reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up
D
reflection across the y-axis, vertical stretching by a factor of 2, vertical translation 3 units down
3

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
4

Which function describes the graph below?

Question illustration
A
y = 8 cosine (x) + 3
Option A
B
y = 4 cosine (x) + 3
Option B
C
y = 4 sine (x) + 3
Option C
D
y = 8 sine (x) + 3
Option D
5

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
6

Which function describes the graph shown below?

Question illustration
A
y = one-half sine (x) minus 2
Option A
B
y = 2 sine (x) minus one-half
Option B
C
y = one-half cosine (x) minus 2
Option C
D
y = 2 cosine (x) minus one-half
Option D
8

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

A
Negative 2 pi
Option A
B
–1
C
1
D
2 pi
Option D
10

What is the domain of f(x) = cos(x)?

A
the set of real numbers
Option A
B
the set of real numbers
Option B
C
the set of real numbers
Option C
D
the set of all real numbers
11

Which set of transformations is needed to graph f(x) = –2sin(x) + 3 from the parent sine function?

A
vertical compression by a factor of 2, vertical translation 3 units up, reflection across the y-axis
B
vertical compression by a factor of 2, vertical translation 3 units down, reflection across the x-axis
C
reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up
D
reflection across the y-axis, vertical stretching by a factor of 2, vertical translation 3 units down
12

What is the range of y = –5sin(x)?

A
all real numbers
Option A
B
all real numbers
Option B
C
all real numbers
Option C
D
all real numbers
Option D
13

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

A
the set of all real numbers
Option A
B
the set of all real numbers
Option B
C
the set of all real numbers
Option C
D
the set of all real numbers
14

Which of the following is true for f(x) = 5cos(x) +1?

A
The period of the function is .
Option A
B
The function has an amplitude of 2.5.
C
A zero of the function is .
Option C
D
The range of the function is the set of real numbers .
Option D
15

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)
16

Which formula gives the x-coordinates of the maximum values for y = cos(x)?

A
for any integer k
Option A
B
for
Option B
C
for any positive integer k
Option C
D
for
Option D
17

Which function describes the graph below?

Question illustration
A
y = 8 cosine (x) + 3
Option A
B
y = 4 cosine (x) + 3
Option B
C
y = 4 sine (x) + 3
Option C
D
y = 8 sine (x) + 3
Option D

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