Question

What are the vertical asymptotes of `f(x) = (2)/(x^2 - 1)`?

Answer 1

Vertical asymptotes for this function will occur when the denominator is negative. Therefore, it behooves us to find the zeroes of the function in the denominator, namely `x^2 -1`. Factoring, we get `x^2-1 = (x-1)(x+1)` and thus our zeroes occur at `x=+-1`. Ergo, the locations of our vertical asymptotes are also `x=+-1`.

For a more thorough explanation of the concept of vertical asymptotes, go here: http://socratic.org/questions/what-is-a-vertical-asymptote-in-calculus?