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What are the horizontal asymptote rules?

Answer 1

To get horizontal asymptotes you must calculate two limits twice. Your asymptote is represented as line #f(x) = ax+b#, where #a = lim_(x->infty) f(x)/x# #b = lim_(x->infty) f(x)-ax#

And the same limits must be calulacted in negative infinity to get appropiate result.

If more explanation needed - write in comments. I would add example later.

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Answer 2

Emma Aldridge

The horizontal asymptote rules are as follows:

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients.
If the degree of the numerator is greater than the degree of the denominator by 1, there is no horizontal asymptote. Instead, there is a slant asymptote, which can be found using long division or synthetic division.
If the degree of the numerator is greater than the degree of the denominator by more than 1, there is no horizontal or slant asymptote.

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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.