# How do you find the domain and range of y=2^(-x) ?

Dec 16, 2017

Domain: $x \in \mathbb{R}$
Range: $\left\{y | 0 \le y\right\}$

#### Explanation:

The function is defined for all real numbers, so the domain is:
$\left\{x \in \mathbb{R}\right\}$

Since the value of any exponential with a positive base can never be $0$, and the function goes to positive infinity, we can using the fact that it is continuous on this interval conclude that the range must be:
$\left\{y | 0 \le y\right\}$