Answer
Domain: $(-\infty,\infty)$
Range: $(-\infty,0)$
Asymptote: $y=0$
Work Step by Step
We are given the function:
$$f(x)=-e^{-x}.$$
Consider the function $f_0(x)=e^x$ as the parent function.
First we obtain the graph of $f_1(x)=e^{-x}$ by reflecting the graph of $f_0$ across the $y$-axis.
Then we reflect the graph of $f_1$ across the $x$-axis to obtain the graph of $f(x)=-e^{-x}$ (see the graph).
From the graph we determine the following elements of function $f$:
- the domain:
$$\text{domain}=(-\infty,\infty)$$
- the range:
$$\text{range}=(-\infty,0)$$
- the horizontal asymptote:
$$y=0.$$
