Answer
(a) See graph. $(-\infty,\infty)$, $(2,\infty)$, $y=2$.
(b) $ g^{-1}(x)=log_3(x-2)$. $(2,\infty)$, $(-\infty,\infty)$, $x=2$.
(c) See graph.
Work Step by Step
(a) To obtain the graph of $g(x)=3^x+2$ from $y=3^x$, shift the curve 2 units up. See graph. We can identify the domain as $(-\infty,\infty)$, range as $(2,\infty)$, horizontal asymptote $y=2$.
(b) Find the inverse $g(x)=3^x+2 \longrightarrow y=3^x+2 \longrightarrow x=3^y+2 \longrightarrow y=log_3(x-2) \longrightarrow g^{-1}(x)=log_3(x-2)$. We can identify the domain as $(2,\infty)$, range as $(-\infty,\infty)$, vertical asymptote $x=2$.
(c) See graph.
