IXL - Match exponential functions and graphs (Algebra 2 practice)

Match each exponential function to its graph.

(

)

(

)

(

)

(

)

(

)

–

(

)

–

ref_doc_title.

Learn with an example

question

Match each exponential function to its graph.

(

)

(

)

(

)

–

(

)

(

)

(

)

–

key idea

This is an equation for an exponential function:

(

)

(

)

Consider

to be the parent function where

is the growth or decay factor.

If
b
>
1
,
the function is growing.
If
0
<
b
<
1
,
the function is decaying.
The graph has a horizontal asymptote of
y
=
0
.

The constant

transforms

If
absolute value bar
a
absolute value bar
>
1
,
the graph is vertically stretched by a factor of
absolute value bar
a
absolute value bar
.
If
absolute value bar
a
absolute value bar
<
1
,
the graph is vertically compressed by a factor of
absolute value bar
a
absolute value bar
.
If
a
<
0
,
the function is also reflected over the
x
-axis.

solution

First, notice that each function is a transformation of either

r
(
x
)
=
4
(
3
)
x
s
(
x
)
=
–
4
(
3
)
x
w
(
x
)
=
4
i
1
3
i
x
m
(
x
)
=
–
4
i
1
3
i
x

It is helpful to sketch the graphs of

and

Consider

first. It includes the point

(

)

has an asymptote of

and grows by a factor of 3.

Next, use the value of

to match

(

)

and

(

)

to their graphs.

To find the graph of

(

)

(

)

apply this transformation to

Vertical stretch by a factor of 4

The graph of

(

)

includes the point

(

)

and has an asymptote of

To find the graph of

(

)

–

(

)

apply this sequence of transformations to

Vertical stretch by a factor of 4
Reflection over the
x
-axis

The graph of

(

)

includes the point

(

–

)

and has an asymptote of

Now consider

It includes the point

(

)

has an asymptote of

and has a decay factor of

Finally, use the value of

to match

(

)

and

(

)

to their graphs.

To find the graph of

(

)

apply this transformation to

Vertical stretch by a factor of 4

The graph of

(

)

includes the point

(

)

and has an asymptote of

To find the graph of

(

)

–

apply this sequence of transformations to

Vertical stretch by a factor of 4
Reflection over the
x
-axis

The graph of

(

)

includes the point

(

–

)

and has an asymptote of

Looking for more? Try these:

Lesson: Exponential functions

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V.3Match exponential functions and graphs I

Z.4Graph exponential functions

Lesson: Exponential functions

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