# What is the domain and range of f(x) =e^x?

Jun 21, 2018

See below.

#### Explanation:

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

This function is valid for all real $x$, so the domain is:

color(blue)({x in RR}

Or in interval notation:

color(blue)((-oo,oo)

To find the range we observe what happens as $x$ approaches $\pm \infty$

as: $x \to \infty$ , $\textcolor{w h i t e}{8888} {e}^{x} \to \infty$

as: $x \to - \infty$ , $\textcolor{w h i t e}{8888} {e}^{x} \to 0$

( i.e if x is negative we have bb(1/(e^x))

We also observe that ${e}^{x}$ can never equal zero.

So our range is:

color(blue)({f(x) in RR | 0 < x}

Or

color(blue)((0,oo)

This is confirmed by the graph of $f \left(x\right) = {e}^{x}$

graph{y=e^x [-16.02, 16.01, -8.01, 8.01]}