Chapter 5.3, Problem 53AYU

In Problems 55-62, begin with the graph of $y=e^x$ (Figure 31) and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

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

To determine

To find: The domain, range and horizontal asymptote of $f\left(x\right)$.

Answer to Problem 53AYU

Solution:

Domain: $\left(-\infty , \infty \right)$.

Range: $\left(0, \infty \right)$.

Horizontal asymptote: $y=0$.

Explanation of Solution

Given:

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

$x$	$f\left(x\right)$
$-2$	$7.3891$
$-1$	$2.7183$
$0$	$1$
$1$	$0.3679$
$2$	$0.1353$

Domain: $\left(-\infty , \infty \right)$.

Range: $\left(0, \infty \right)$.

Horizontal asymptote: $y=0$.