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

1 Answer
May 2, 2018

Answer:

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]}