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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#

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Answer 2

Aurora Alvarado

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. This happens when the denominator of a rational function becomes zero at that value, resulting in an undefined value.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.