Question

For what values of x, if any, does `f(x) = tan((pi)/4-9x)` have vertical asymptotes?

Answer 1

Period: `pi/9`. For each period `(pi/12+k/9pi, 7/36pi+k/9pi)`, there are two terminal asymptotes x = end value, `k = 0, +-1, +-2, +-3, ...`

Explanation:

As `(pi/4-9x) to` (an odd multiple ) `(2k+1)` of `pi/2`,`f to +-oo`,

giving

`f to +-oo`, as `x to -(4k+1)/36pi, k = 0, +-1, +-2, +-3, ..`

So, in ine period `x in (pi/12, 7/36pi)`, we have two terminal

asymptotes

`x = pi/12 and x = 7/36pi`

The period for f is `pi/9=(7/36-1/12)pi`.

graph{y-tan(0.7854-9x)=0 [-5, 5, -2.5, 2.5]}