Answer
See graph; asymptote $y=2$
Domain: $(-\infty,\infty)$ and range: $(2,\infty)$
Work Step by Step
Step 1. Start from the original function $f(x)=e^x$ shown as the green curve in the figure.
Step 2. To obtain the new curve of $h(x)=e^{x/2}+2$, stretch the original horizontally by a factor of 2, then shift the result vertically 2 units up to get the red curve as shown.
Step 3. We can identify the new asymptote as $y=2$
Step 4. We can determine the domain as $(-\infty,\infty)$ and range as $(2,\infty)$
