Question

What makes a vertical asymptote?

Answer 1

If `x=a` is a vertical asymptote of a function `f(x)`, then it means that the graph of `f` displays a "blowing-up" or a "Blowing-down" behavior there, that is, either the left-hand limit or the right-hand limit (or both) must be an infinite limit.

`lim_{x to a^-}f(x)=pm infty` or `lim_{x to a^+}f(x)=pm infty`

I hope that this was helpful.