IXL - Match exponential functions and graphs (Geometry practice)

Match each exponential function to its graph.

(

)

2.5

(

1.5

)

(

)

–

(

1.5

)

(

)

2.5

(

0.5

)

(

)

–

(

0.5

)

ref_doc_title.

Learn with an example

question

Match each exponential function to its graph.

(

)

(

0.5

)

(

)

(

0.5

)

–

(

)

0.5

(

)

0.5

–

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 constants

and

transform

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.
The graph is then shifted vertically
absolute value bar
k
absolute value bar
units. It shifts up if
k
>
0
and down if
k
<
0
.
The horizontal asymptote is also shifted, so its equation is
y
=
k
.

solution

First, notice that each function is a transformation of

0.5

h
(
x
)
=
3
(
0.5
)
x
+
2
p
(
x
)
=
3
(
0.5
)
x
–
2
m
(
x
)
=
0.5
x
+
2
t
(
x
)
=
0.5
x
–
2

It is helpful to sketch the graph of

0.5

It includes the point

(

)

has an asymptote of

and has a decay factor of 0.5.

Next, use the values of

and

to match each function to its graph.

To find the graph of

(

)

(

0.5

)

apply this sequence of transformations to

0.5

Vertical stretch by a factor of 3
Shift 2 units up

The graph of

(

)

includes the point

(

)

and has an asymptote of

To find the graph of

(

)

(

0.5

)

–

apply this sequence of transformations to

0.5

Vertical stretch by a factor of 3
Shift 2 units down

The graph of

(

)

includes the point

(

)

and has an asymptote of

–

To find the graph of

(

)

0.5

apply this transformation to

0.5

Shift 2 units up

The graph of

(

)

includes the point

(

)

and has an asymptote of

To find the graph of

(

)

0.5

–

apply this transformation to

0.5

Shift 2 units down

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

Lesson: Exponential functions

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