Question

How do you graph `y=-tan2x` and include two full periods?

Answer 1

Create a normal tan graph:
graph{tan(x) [-0.5, 6.29, -4, 4]}
(If you don't know how, then either think of how tan changes as the angle of the triangle increases from zero, or remember this chart:

`0` : `0`
`pi/4` : `1`
`pi/2` : undefined (goes off to infinity)
`(3pi)/4` : `-1`
`pi` : `0`
Repeat this at least twice.)

Then compress it in the horizontal by a factor of two (because of the `2x` in the tan:
graph{tan(2x) [-0.5, 6.29, -4, 4]}
Then flip it on the vertical (because of the negative sign):
graph{-tan(2x) [-0.5, 6.29, -4, 4]}

The graph must show at least `pi`, since the period of `tan(x)` is pi, which was divided in two by the 2x inside the tan, then multiplied because you need to show two periods