Answer
Domain: $x\lt3$ or $(-∞,3)$
x-intercept: $(2,0)$
$x=3$ is the vertical asymptote.
Work Step by Step
$f(x)=\ln(3-x)$
Domain:
$3-x\gt0$
$-x\gt-3$
$x\lt3$ or $(-∞,3)$
x-intercept:
$f(x)=\ln(3-x)=0$
$e^{\ln(3-x)}=e^0~~$ (Using the Inverse Property $e^{\ln x}=x$):
$3-x=1$
$-x=-2$
$x=2~~$ So, the x-intercept point is $(2,0)$
$\ln (3-x)→-∞$ when $3-x→0^+$, that is, when $-x→-3^+$, or when $x→3^-$.
Then $x=3$ is the vertical asymptote.
