Answer
Domain: $x\gt6$ or $(6,∞)$
x-intercept: $(7,0)$
Then $x=6$ (y-axis) is the vertical asymptote.
Work Step by Step
$h(x)=\ln(x-6)$
Domain: $x-6\gt0$, that is, $x\gt6$ or $(6,∞)$
x-intercept:
$h(x)=\ln(x-6)=0$
$e^{\ln(x-6)}=e^0$ (Using the Inverse Property $e^{\ln x}=x$):
$x-6=1$
$x=7~~$So, the x-intercept point is $(7,0)$
$\ln(x-6)→−∞$ when $x-6→0^+$, that is, when $x→6^+$. Then $x=6$ (y-axis) is the vertical asymptote.
