Answer
$\text{Domain: }
(-\infty, \infty)
\\\text{Range: }
(1,\infty)
\\\text{Horizontal Asymptote: }
y=1$
Work Step by Step
The black graph is the graph given in Figure 2, $y=
2^x
$.
The red graph is the graph of the given function, $
f(x)=2^{x-4}+1
$. It is the result of shifting the black graph by $3$ units to the right and $1$ unit up.
The red graph has the following characteristics:
\begin{array}{l}\require{cancel}
\text{Domain: }
(-\infty, \infty)
\\\text{Range: }
(1,\infty)
\\\text{Horizontal Asymptote: }
y=1
.\end{array}
