Question

What are the important information needed to graph `y=tan(2x)`?

Answer 1

Please see below.

Explanation:

A typical graph of `tanx` has domain for all values of `x` except at `(2n+1)pi/2`, where `n` is an integer (we have asymptotes too here) and range is from `[-oo,oo]` and there is no limiting (unlike other trigonometric functions other than tan and cot). It appears like graph{tan(x) [-5, 5, -5, 5]}

The period of `tanx` is `pi` (i.e. it repeats after every `pi`) and that of `tanax` is `pi/a` and hence for `tan2x` period will be `pi/2`

Hencem the asymptotes for `tan2x` will be at each `(2n+1)pi/4`, where `n` is an integer.

As the function is simply `tan2x`, there is no phase shift involved (it is there only if function is of the type `tan(nx+k)`, where `k` is a constant. Phase shift causes graph pattern to shift horizontally to left or right.

The graph of `tan2x` appears like graph{tan(2x) [-5, 5, -5, 5]}