Answer
Domain: $(-\infty,\infty)$
Range: $(4,\infty)$
Asymptote: $y=4$
Work Step by Step
We are given the function:
$$f(x)=e^{x-4}+4.$$
Consider the function $f_0(x)=e^x$ as the parent function.
First we obtain the graph of $f_1(x)=e^{x-3}$ by horizontally shifting the graph of $f_0$ by $3$ units to the right.
Then we obtain the graph of $f(x)=e^{x-3}+4$ by vertically shifting the graph of $f_1$ by $4$ units up (see the graph).
From the graph we determine the following elements of function $f$:
- the domain:
$$\text{domain}=(-\infty,\infty)$$
- the range:
$$\text{range}=(4,\infty)$$
- the horizontal asymptote:
$$y=4.$$
