Question

How do you find the vertical asymptotes of f(x) = tan(πx)?

Answer 1

The vertical asymptotes occur whenever `x=k+1/2,kinZZ`.

Explanation:

The vertical asymptotes of the tangent function and the values of `x` for which it is undefined.

We know that `tan(theta)` is undefined whenever `theta=(k+1/2)pi,kinZZ`.

Therefore, `tan(pix)` is undefined whenever `pix=(k+1/2)pi,kinZZ`, or `x=k+1/2,kinZZ`.

Thus, the vertical asymptotes are `x=k+1/2,kinZZ`.

You can see more clearly in this graph:

graph{(y-tan(pix))=0 [-10, 10, -5, 5]}