Answer
The domain: $x\gt-2$.
The x-intercept: $x=-1$.
The vertical asymptote: $x=-2$.
See graph
Work Step by Step
$$f(x)=-\log_{6}(x+2)$$ The function is defined when:
$$x+2\gt0$$ $$x\gt-2$$ Thus, the domain is $x\gt-2$. Finding the $x$-intercept, set $f(x)=0$:
$$0=-\log_{6}(x+2)$$ $$\log_{6}(x+2)=0$$ Rewriting in exponential form:
$$x+2=6^0$$ $$x+2=1$$ $$x=-1$$
Thus, the x-intercept is $x=-1$.
Based from the domain, the vertical asymptote is:
$$x=-2$$
The sketch of the graph is as shown.
