IXL - Graph translations of sine and cosine functions (Precalculus practice)

Graph the function

(

)

cos

(

)

Coordinate plane graph with 4 quadrants, x-axis coordinates from -6.283185307179586 to 6.283185307179586, y-axis coordinates from -5 to 5.

ref_doc_title.

Learn with an example

question

Graph the function

(

)

cos

(

)

key idea

This is the graph of

cos

(

)

The graph of

cos

(

)

is similar to the graph of

cos

(

)

The numbers

and

determine the characteristics of the graph.

absolute value bar
A
absolute value bar
is the
amplitude.
It is half the vertical distance from the graph's maximum to its minimum.
2
pi
absolute value bar
B
absolute value bar
is the
period.
It is the horizontal distance between two consecutive maxima.
–
C
absolute value bar
B
absolute value bar
is the phase
shift.
It is the horizontal shift that takes
A
cos
(
B
x
)
+
D
to
A
cos
(
B
x
+
C
)
+
D
.
y
=
D
is the
midline.
It is a horizontal line that cuts the graph in half.
D
is the vertical
shift.
Its absolute value,
|
D
|,
is the vertical distance between the midline and the
x
-axis.

solution

Transform the graph of

cos

(

)

into the graph of

cos

(

)

Begin with the graph of

cos

(

)

Find the period.

Period

The period is

Since this equals the period of

cos

(

)

the graph remains the same at this step.

Find the phase shift.

Phase shift

–

Since the phase shift is 0, the graph does not change at this step.

Find the vertical shift.

Vertical shift

This vertical shift is 1, so shift the graph of

cos

(

)

up by 1. This is the graph of the original function,

(

)

cos

(

)

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Work it out

Not feeling ready yet? These can help:

S.5Graph translations of sine functions

S.10Graph translations of cosine functions

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