Answer
Domain: $x\gt4$ or $(4,∞)$
x-intercept: $(5,0)$
$x=4$ is the vertical asymptote.
Work Step by Step
$f(x)=\ln(x-4)$
Domain:
$x-4\gt0$
$x\gt4$ or $(4,∞)$
x-intercept:
$f(x)=\ln(x-4)=0$
$e^{\ln(x-4)}=e^0~~$ (Using the Inverse Property $e^{\ln x}=x$):
$x-4=1$
$x=5~~$ So, the x-intercept point is $(5,0)$
$\ln (x-4)→-∞$ when $x-4→0^+$, that is, when $x→4^+$.
Then $x=4$ is the vertical asymptote.
