# What is the domain and range of y=4^x?

May 8, 2016

Domain: All Real values
Range: All Real values greater than zero.

#### Explanation:

${4}^{x}$ is defined for all Real values of $x$
$\textcolor{w h i t e}{\text{XXX}}$Domain($x$) $= \mathbb{R}$

$y = {4}^{x}$ approaches $0$ as $x \rightarrow - \infty$
$\textcolor{w h i t e}{\text{XXX}}$and approaches $+ \infty$ as $x \rightarrow + \infty$
It is continuous in this range (takes on all possible values).
Therefore Range($y$) $= \left(0 , + \infty\right) \in \mathbb{R}$