Answer
Domain: $x\gt-4$ or $(-4,∞)$
x-intercept: $(-3,0)$
Then $x=-4$ is the vertical asymptote.
Work Step by Step
$f(x)=\ln(x+4)$
Domain: $x+4\gt0$, that is, $x\gt-4$ or $(-4,∞)$
x-intercept:
$f(x)=\ln(x+4)=0$
$e^{\ln(x+4)}=e^0$ (Using the Inverse Property $e^{\ln x}=x$):
$x+4=1$
$x=-3~~$So, the x-intercept point is $(-3,0)$
$\ln(x+4)→−∞$ when $x+4→0^+$, that is, when $x→-4^+$. Then $x=-4$ is the vertical asymptote.
