The graph of the function $f(x)=\log_3 (x-2)$ can be obtained from the graph of $g(x)=\log_3 x$ by one of the following actions:
(a) shifting the graph of $g(x)$ to the right 2 units;
(b) shifting the graph of $g(x)$ to the left 2 units;
(c) shifting the graph of $g(x)$ upward 2 units;
(d) shifting the graph of $g(x)$ downward 2 units;
Your answer is (input a, b, c, or d)

The domain of the function $f(x)$ is .
Note: Enter your answer using interval notation.

The range of the function $f(x)$ is .
Note: Enter your answer using interval notation.

The $x$-intercept of the function $f(x)$ is .

The vertical asymptote of the function $f(x)$ has equation: .