Answer
Domain: $(-\infty,\infty)$
Range: $(0,\infty)$
Asymptote: $y=0$
Work Step by Step
We are given the function:
$$f(x)=e^{x-2}.$$
Consider the function $f_0(x)=e^x$ as the parent function. We obtain the graph of $f$ by horizontally shifting the graph of $f_0$ by $2$ units to the right (see the graph).
From the graph we determine the following elements of function $g$:
- the domain:
$$\text{domain}=(-\infty,\infty)$$
- the range:
$$\text{range}=(0,\infty)$$
- the horizontal asymptote:
$$y=0.$$
