Answer
Domain: $(-\infty,\infty)$
Range: $(-\infty,1)$
Asymptote: $y=1$
Work Step by Step
We are given the function:
$$f(x)=1-e^x.$$
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 $f_0$ about the $x$-axis.
Then we vertically shift the graph of $f_1$ by $1$ unit up to get the graph of $f(x)=1-e^x$ (see the graph).
From the graph we determine the following elements of function $f$:
- the domain:
$$\text{domain}=(-\infty,\infty)$$
- the range:
$$\text{range}=(-\infty,1)$$
- the horizontal asymptote:
$$y=1.$$