Question

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

Answer 1

You are changing a function by adding something to its argument, i.e., you're passing from `f(x)` to `f(x+k)`.

This kind of changes affects the graph of the original function in terms of a horizontal shift: if `k` is positive, the shift is toward the left, and vice versa if `k` is negative, the shift is to the right.

So, since in our case the original function is `f(x)=tan(x)`, and `k=pi/3`, we have that the graph of `f(x+k)=tan(x+pi/3)` is the graph of `tan(x)`, shifted `pi/3` units to the left.