AnswersAZ-Common Core Algebra II BGraphing Sine and Cosine

Graphing Sine and Cosine Answers

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1
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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
2
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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
3

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
4

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

A
Negative 2 pi
Option A
B
–1
C
1
D
2 pi
Option D
5

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
6

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)
7

Which function has the given properties below?The domain is the set of all real numbers.One x-intercept is .The maximum value is 3.The y-intercept is (0, –3).

Question illustration
A
y = –3sin(x)
B
y = –3cos(x)
C
y = 3sin(x)
D
y = 3cos(x)
8

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
9

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)
10

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
11

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
12

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)
13

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
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

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

A
Negative 2 pi
Option A
B
–1
C
1
D
2 pi
Option D
16

Which function has the given properties below?The domain is the set of all real numbers.One x-intercept is .The maximum value is 3.The y-intercept is (0, –3).

Question illustration
A
y = –3sin(x)
B
y = –3cos(x)
C
y = 3sin(x)
D
y = 3cos(x)
17

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
18

The graph of which function passes through (0,4) and has a minimum value at ?

Question illustration
A
f (x) = sine (x) + 4
Option A
B
f (x) = cosine (x) + 3
Option B
C
f (x) = negative 3 sine (x)
Option C
D
f (x) = 4 cosine (x)
Option D
19

What is the amplitude of the function below?

Question illustration
A
1
B
2
C
Pi
Option C
D
2 pi
Option D
20

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

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