Answer
Domain: $(-\infty,\infty)$
Range: $(-1,\infty)$
Asymptote: $y=-1$
Work Step by Step
We are given the function:
$$h(x)=e^{-x}-1.$$
Consider the function $f(x)=e^x$ as the parent function.
First we obtain the graph of $g(x)=e^{-x}$ by reflecting the graph of $f$ across the $y$-axis.
Then we vertically shift the graph of $g$ by $1$ unit down to obtain the graph of $h(x)=e^{-x}-1$ (see the graph).
From the graph we determine the following elements of function $h$:
- the domain:
$$\text{domain}=(-\infty,\infty)$$
- the range:
$$\text{range}=(-1,\infty)$$
- the horizontal asymptote:
$$y=-1.$$