Answer
See below.
Work Step by Step
Step 1. To obtain the graph of $f(x)=9-3e^{-x}$ from $y=e^{x}$, reflect the curve across the y-axis, stretch vertically by a factor of 3, reflect across the x-axis, and then shift 2 units up. See graph.
Step 2. We can determine the domain is $(-\infty,\infty)$; the range is $(-\infty,9)$; and the horizontal asymptote is $y=9$.