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