Answer
Domain :$\qquad($0$,+\infty)$
Range :$\qquad(-\infty,+\infty)$
Vertical asymptote: $\qquad x=$0
Work Step by Step
We start with the graph of $f_{1}(x)=\log_{3}(x)$ (dashed blue).
Since y$=2+\log_{3}(x)=f(x)+2$
its graph (red) is obtained by
shifting $f_{1}(x)$ up by 2 units.
Domain :$\qquad($0$,+\infty)$
Range :$\qquad(-\infty,+\infty)$
Vertical asymptote: $\qquad x=$0