Answer
See graph
Domain: $(-\infty,\infty)$
Range: $(1,\infty)$
Horizontal asymptote: $y=1$
Work Step by Step
We are given the function:
$f(x)=3^{x-2}+1$
We start graphing the parent function $a(x)=3^x$.
We horizontally shift $a(x)$ 2 units to the right to get $b(x)=3^{x-2}$.
Finally vertically shift $b(x)$ one unit upward to get $f(x)=3^{x-2}+1$.
Determine the domain:
$(-\infty,\infty)$
Determine the range:
$3^{x-2}>0$
$3^{x-2}+1>0+1$
$f(x)>1$
$(1,\infty)$
As $x\rightarrow -\infty,f(x)\rightarrow 1$
Therefore there is a horizontal asymptote:
$y=1$
