Question

Find the asymptotes of p(x)=tan(x-pi/8)

Answer 1

Explanation:

As far as the 2 asymptotes shown, here is how we would find them. Take the argument,
`(x-(\pi )/(8))`, and set it equal to the parent asymptotes of
`(\pi )/(2)` and

`-(\pi )/(2)` and solve for x. These will give you the locations of the translated asymptotes.

`x-(\pi )/(8)=(\pi )/(2)` and

`x=(\pi )/(8)+(4\pi )/(8)` so

`x=(5\pi )/(8)`. That's the vertical asymptote on the right. For the one on the left,

`x-(\pi)/(8)=-(\pi)/(2)` and

`x=(\pi)/(8)-(4\pi)/(8)` so

`x=-(3\pi)/(8)`.

As far as the general solution goes,

`x=(5\pi)/(8)+/-k\pi`