# How do you graph y=4^(x-2)-1?

Dec 20, 2017

The graph of $y$ is the standard exponential increasing graph of $f \left(x\right) = {4}^{x}$ scaled by $\frac{1}{16}$ and shifted one unit negative ("down") on the $y -$axis.

#### Explanation:

$y = {4}^{x - 2} - 1$

We can rewrite $y$ as: $y = {4}^{x} / {4}^{2} - 1$

$y = \frac{1}{16} \cdot {4}^{x} - 1$

Consider the standard exponential increasing graph of $f \left(x\right) = {4}^{x}$ below.

graph{4^x [-10, 10, -5, 5]}

We can now see that the graph of $y$ is the graph of $f \left(x\right) = {4}^{x}$ scaled by $\frac{1}{16}$ and shifted one unit negative ("down") on the $y -$axis. As below:

graph{4^(x-2) -1 [-10, 10, -5, 5]}