# How do you use the graph of f(x)=3^x to describe the transformation of g(x)=3^(x-4)?

Jun 21, 2017

$g \left(x\right)$ is $f \left(x\right)$ scaled by $\frac{1}{81}$

#### Explanation:

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

$g \left(x\right) = {3}^{x - 4}$

$= {3}^{x} \times {3}^{- 4} = {3}^{x} / {3}^{4}$

$= f \frac{x}{3} ^ 4 = f \frac{x}{81}$

Hence, $g \left(x\right)$ is $f \left(x\right)$ scaled by $\frac{1}{81}$

The graph of $f \left(x\right)$ is shown below.
graph{3^x [-7.9, 7.905, -3.95, 3.95]}