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