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