AnswersCMS 2026-2027 NC Math 3 CREDIT RECOVERYGraphing Sine and Cosine

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What is the domain of f of x is equal to cosine of x ?

A
the set of real numbers negative 1 is less than or equal to x comma x is less than or equal to 1
B
the set of real numbers 0 is less than or equal to x comma x is less than or equal to 2 pi
C
the set of all real numbers
D
the set of real numbers negative 2 pi is less than or equal to x comma x is less than or equal to 2 pi
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What is the range of y is equal to negative 5 sine x ?

A
all real numbers negative 5 halves is less than or equal to y comma y is less than or equal to 5 halves
B
all real numbers negative 1 fifth is less than or equal to y comma y is less than or equal to 1 fifth
C
all real numbers negative 5 is less than or equal to y comma y is less than or equal to 5
D
all real numbers negative 1 is less than or equal to y comma y is less than or equal to 1
3

Which function has the given properties? The domain is the set of all real numbers. One x -intercept is open paren 2 pi comma 0 close paren The amplitude is 4 The point open paren pi over 2 comma negative 4 close paren is on the graph. The y -intercept is open paren 0 comma 0 close paren

A
y is equal to 4 cosine x
B
y is equal to negative 4 cosine x
C
y is equal to 4 sine x
D
y is equal to negative 4 sine x
4

Which function has the given properties? The domain is the set of all real numbers. One x -intercept is open paren pi over 2 comma 0 close paren The maximum value is 3 The y -intercept is open paren 0 comma negative 3 close paren

A
y is equal to 3 sine x
B
y is equal to negative 3 sine x
C
y is equal to negative 3 cosine x
D
y is equal to 3 cosine x
5

Which formula gives the x -coordinates of the maximum values for y is equal to cosine of x ?

A
k pi over 2 for any positive integer k
B
k pi over 2 for k is equal to 0 comma plus or minus 2 comma plus or minus 4 comma ...
C
k pi for k is equal to 0 comma plus or minus 2 comma plus or minus 4 comma ...
D
k pi for any integer k
6

What is the range of f of x is equal to sine of x ?

A
the set of all real numbers 0 is less than or equal to y comma y is less than or equal to 2 pi
B
the set of all real numbers negative 2 pi is less than or equal to y comma y is less than or equal to 2 pi
C
the set of all real numbers negative 1 is less than or equal to y comma y is less than or equal to 1
D
the set of all real numbers
7

Which of the following is true for f of x is equal to 5 cosine x plus 1 ?

A
The range of the function is the set of real numbers negative 4 is less than or equal to y comma y is less than or equal to 6 .
B
The period of the function is 10 pi .
C
A zero of the function is open paren pi over 2 comma 0 close paren .
D
The function has an amplitude of 2 point 5 .
8

What is the period of f of x is equal to sine of x ?

A
pi over 2
B
3 pi over 2
C
pi
D
2 pi
9

Which set of transformations is needed to graph f of x is equal to negative 2 sine x plus 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
reflection across the x -axis, vertical stretching by a factor of 2 , vertical translation 3 units up
C
reflection across the y -axis, vertical stretching by a factor of 2 , vertical translation 3 units down
D
vertical compression by a factor of 2 , vertical translation 3 units down, reflection across the x -axis
10

What is the maximum of f of x is equal to sine of x ?

A
1
B
negative 1
C
2 pi
D
negative 2 pi

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