Answer
See below.
Work Step by Step
Step 1. To obtain the graph of $f(x)=2-e^{-x/2}$ from $y=e^{x}$, stretch the curve horizontally by a factor of 2, reflect across the y-axis, 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 $(-\infty,2)$; and the horizontal asymptote is $y=2$.