What are the important information needed to graph y = tan (1/3 x)?

Period is the important information required. It is $3 \pi$ in this case.
Important information for graphing tan ($\frac{1}{3}$ x) is the period of the function. Period in this case is $\frac{\pi}{\frac{1}{3}}$ = $3 \pi$. The graph would thus be similar to that of tan x, but spaced at intervals of $3 \pi$