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Mathematics-Online course: Prepcourse Mathematics - Analysis - Extrema and Curve Sketching

Asymptotes of Rational Functions

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A rational function

ALT=

has a linear asymptote, iff deg ALT=   deg ALT=.

For deg ALT=   deg ALT= it is

ALT=

i.e. the ALT=-axis is r's asymptote.

For deg ALT=   deg ALT=   deg ALT= the asymptote can be determined via long (polynomial) division:

ALT=

with deg ALT=   deg ALT= . The asymptote is horizontal ALT=, if degALT=   deg ALT=. Examples are illustrated in the following.

ALT=          ALT=          ALT=

If the numerator's degree is more than 1 greater than the denominator's degree, then ALT= has an at least quadratic asymptote.

(Authors: Höllig/Hörner/Abele)
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  automatically generated 9/18/2007