What does vertical asymptote mean?

1 Answer
Sep 25, 2014

A vertical line x=ax=a is called a vertical asymptote of a function f(x)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)}.

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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.