Answer
The domain: $x\gt0$.
The $x$-intercept: $(7,0)$.
The vertical asymptote: $x=0$.
See graph
Work Step by Step
$$f(x)=\log \frac{x}{7}$$ The function is defined when:
$$\frac{x}{7}\gt0$$ $$x\gt0$$ Thus, the domain is $x\gt0$.
Finding the $x$-intercept, set $f(x)=0$:
$$0=\log \frac{x}{7}$$ $$\log \frac{x}{7}=0$$
Rewriting in exponential form:
$$\frac{x}{7}=10^{0}$$ $$\frac{x}{7}=1$$ $$x=7$$
Thus, the $x$-intercept is $(7,0)$.
Based from the domain, the vertical asymptote is:
$$x=0$$ The sketch of the graph is as shown.
