# How do you graph f(x)=4^(x-2) and state the domain and range?

Aug 31, 2017

domain is $\left\{x \in \mathbb{R}\right\}$
range is $\left\{y \in {\mathbb{R}}^{+} : y \ne 0\right\}$

#### Explanation:

$f \left(x\right) = {4}^{x - 2}$ is a continuous function for all $\mathbb{R}$
So domain is $\left\{x \in \mathbb{R}\right\}$

${4}^{x - 2}$ can never equal 0.

If $x \ge 2$ then ${4}^{x - 2} \ge 1$

If $x < 2$ then ${4}^{x - 2}$ = 1/(4^(2 - x)

As $x \to - \infty$ then $\frac{1}{{4}^{2 - x}} \to 0$

So range is $\left\{y \in {\mathbb{R}}^{+} : y \ne 0\right\}$

$y$ axis intercept is $\frac{1}{16}$ where $x = 0$

The $x$ axis is a horizontal asymptote.

graph{y = 4^(x - 2) [-8.89, 8.885, -4.444, 4.44]}