Answer
See below.
Work Step by Step
Step 1. To obtain the graph of $f(x)=7-3e^{2x}$ from $y=e^{x}$, shrink the curve horizontally by a factor of 1/2, stretch vertically by a factor of 3, reflect across the x-axis, and then shift 7 units up. See graph.
Step 2. We can determine the domain is $(-\infty,\infty)$; the range is $(-\infty,7)$; and the horizontal asymptote is $y=7$.
