Question

How do you graph, identify the domain, range, and asymptotes for `y=tan(2x+pi/2)`?

Answer 1

Domain: `x ne k/2pi, k = 0, +- 1, +- 2, +- 3, ..`
Range: `( - oo, oo )`.
Asymptotes: `x = k/2pi, k = 0, +- 1, +- 2, +- 3, ..`. See grapj.

Explanation:

`y = tan ( 2x + pi/2 ) = - cot 2x,`

`x ne 0, +- pi/2, +- pi, +- 3/2 pi, +-2pi, ...`

Graph of `y = tan ( 2x + pi/2 )`:
graph{y-tan(2x+pi/2)=0}