Graphing Exponential Functions

A simple exponential function to graph is

y = 2^{x}

$x$	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$y = 2^{x}$	$\frac{1}{8}$	$\frac{1}{4}$	$\frac{1}{2}$	$1$	$2$	$4$	$8$

Notice that the graph has the

x

-axis as an asymptote on the left, and increases very fast on the right.

Changing the base changes the shape of the graph.

Replacing

x

with

- x

reflects the graph across the

y

-axis; replacing

y

with

- y

reflects it across the

x

-axis.

Replacing

x

with

x + h

translates the graph

h

units to the left.

Replacing

y

with

y - k

(which is the same as adding

k

to the right side) translates the graph

k

units up.

Mrs. Osawaru