Question

On the same coordinate system, graph:

$f\left(x\right)=3^x$

$g\left(x\right)=3^{x+1}$

Short answer

The graph of $f\left(x\right)=3^x$and

$g\left(x\right)=3^{x+1}$on the same coordinate axis is:

Step-by-step solution

Step 1. Given

The function$$\begin{gathered} f\left(x\right)=3^x \\ g\left(x\right)=3^{x+1} \end{gathered}$$

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 $f\left(x\right)=3^x$

$x$	$f\left(x\right)=3^x$	$(x,f(x\left)\right)$
$-2$	$3^{-2}=\frac{1}{9}$	$(-2,\frac{1}{9})$
$-1$	$3^{-1}=\frac{1}{3}$	$(-1,\frac{1}{3})$
$0$	$3^0=1$	$(0,1)$
$1$	$3^1=3$	$(1,3)$
$2$	$3^2=9$	$(2,9)$

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 $g\left(x\right)=3^{x+1}$

$x$	$g\left(x\right)=3^{x+1}$	$(x,g(x\left)\right)$
$-2$	$3^{-2+1}=\frac{1}{3}$	$(-2,\frac{1}{3})$
$-1$	$3^{-1+1}=1$	$(-1,1)$
$0$	$3^{0+1}=3$	$(0,3)$
$1$	$3^{1+1}=9$	$(1,9)$
$2$	$3^{2+1}=27$	$(2,27)$

Step 5. Plot the points in the graph

Plot the obtained points in the graph.