Answer
please see image
Work Step by Step
We start with the graph of $f_{1}(x)=\log_{2}(x)$ (dashed blue).
Since $f(x)=\log_{2}(x-4)=f(x-4)$
its graph is obtained by shifting $f_{1}(x)$ to the right by 4 units.
Domain of $f$:$\qquad(4,+\infty)$
Range of $f$:$\qquad(-\infty,+\infty)$
Vertical asymptote: $\qquad x=4$
