Question

What does vertical asymptote mean?

Answer 1

A vertical line `x=a` is called a vertical asymptote of a function `f(x)` if one of the following is true:

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

Let us look at the vertical asymptotes of

`f(x)=1/{(x+2)(x-3)}`.

As we can see in the graph above,

`lim_{x to -2^-}f(x)=+infty`,

makes `x=-2` (in red) a vertical asymptote, and

`lim_{x to 3^-}f(x)=-infty`,

makes `x=3` (in blue) a vertical aymptote.