Question

Question #ee2f5

Answer 1

Here is the difference. Horizontal asymptotes are defined in terms of limits at infinity, but vertical asymptotes are defined in terms of infinite limits. Please compare the definitions below.

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Horizontal Asymptotes

`y=b` is called a horizontal asymptote of `f(x)` if al least one of the following holds:

`lim_{x to infty}f(x)=b` or `lim_{x to -infty}f(x)=b`

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Vertical Asymptotes

`x=a` is called a vertical asymptote of `f(x)` if at least one of the following holds:

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

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I hope that this was helpful.