Question

On the same coordinate system, graph:

$f\left(x\right)=2^x$

$g\left(x\right)=2^{x-1}$

Short answer

The graph of $f\left(x\right)=2^x$and

$g\left(x\right)=2^{x-1}$on the same coordinate axis is:

Step-by-step solution

Step 1. Given

The function$$\begin{gathered} f\left(x\right)=2^x \\ g\left(x\right)=2^{x-1} \end{gathered}$$

To graph the given function on the same coordinate axes.

Step 2. Table of points for the function f(x)

Find the points for the function $f\left(x\right)=2^x$

$x$	$f\left(x\right)=2^x$	$(x,f(x\left)\right)$
$-2$	$2^{-2}=\frac{1}{4}$	$(-2,\frac{1}{4})$
$-1$	$2^{-1}=\frac{1}{2}$	$(-1,\frac{1}{2})$
$0$	$2^0=1$	$(0,1)$
$1$	$2^1=2$	$(1,2)$
$2$	$2^2=4$	$(2,4)$

Step 3. Plot the points in the graph

Plot the obtained points in the graph.

Step 4. Table of points for the function g(x)

Find the points for the function $g\left(x\right)=2^{x-1}$

$x$	$g\left(x\right)=2^{x-1}$	$(x,g(x\left)\right)$
$-2$	$2^{-2-1}=\frac{1}{8}$	$(-2,\frac{1}{8})$
$-1$	$2^{-1-1}=\frac{1}{4}$	$(-1,\frac{1}{4})$
$0$	$2^{0-1}=\frac{1}{2}$	$(0,\frac{1}{2})$
$1$	$2^{1-1}=1$	$(1,1)$
$2$	$2^{2-1}=2$	$(2,2)$

Step 5. Plot the points in the graph

Plot the obtained points in the graph.