Answer
See graph; asymptote: $y=0$
Domain: $(-\infty,\infty)$ and range: $(-\infty,0)$
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 $h(x)=-e^{x}$, reflect the original with respect to the x-axis to get the red curve as shown.
Step 3. We can identify the asymptote as $y=0$
Step 4. We can determine the domain as $(-\infty,\infty)$ and range as $(-\infty,0)$
