Answer
Domain: $x\lt0$ or $(-∞,0)$
x-intercept: $(-1,0)$
$x=0$ (y-axis) is the vertical asymptote.
Work Step by Step
$g(x)=\ln(-x)$
Domain:
$-x\gt0$
$x\lt0$ or $(-∞,0)$
x-intercept:
$g(x)=\ln(-x)=0$
$e^{\ln(-x)}=e^0~~$ (Using the Inverse Property $e^{\ln x}=x$):
$-x=1$
$x=-1~~$ So, the x-intercept point is $(-1,0)$
$\ln (-x)→-∞$ when $-x→0^+$, that is, when $x→0^-$.
Then $x=0$ (y-axis) is the vertical asymptote.
