Answer
Domain: $x\gt3$ or $(3,∞)$
x-intercept: $(4,0)$
$x=3$ is the vertical asymptote.
Work Step by Step
$h(x)=\log_4(x-3)$
Domain:
$x-3\gt0$
$x\gt3$ or $(3,∞)$
x-intercept:
$h(x)=\log_4(x-3)=0$
$4^0=x-3$
$x-3=1$
$x=4~~$ So, the x-intercept point is $(4,0)$
$\log_ax→-∞$ when $x→0^+$. So, we have that:
$\log_4(x-3)→-∞$ when $x-3→0^+$
$\log_4(x-3)→-∞$ when $x→3^+$.
Then $x=3$ is the vertical asymptote.
