Question

How do you graph `-2 tan^(-1) (x/4)`?

Answer 1

Graphs are inserted and explained.

Explanation:

I have now adopted the convention `tan^(-1)theta in (-pi/2, pi/2)` only.

`y=-2tan^(-1)(x/4) in -2(-pi/2, pi/2)=-(-pi, pi)`,

giving 1 - 1 relation.

Inversely,

`x = -4 tan(y/2),. y in (-pi. pi) and x in (-oo, oo)`.

In the inserted graph, the required graph is restricted to

`y in (-pi. pi)`.

This covers one y-period `(pi)/(1/2) = 2pi`. The terminal asymptotes

are `y=+-pi`.

Graph of `y = -2 tan^(-1) (x/4)`:

graph{x+4tan(y/2)=0[-500 500 -3.4 3.1416]}

Breaking the conventional 1 - 1 rule, 'one x - many y' graph is also presented. The terminal asymptotes are `y = +-k pi, k = 1, 2, 3. 4, ...`. See below.

graph{x+4tan(y/2)=0[-500 500 -20 20]}