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Rational Functions

A rational function is the ratio of two polynomials N(x)/D(x) which have no common factors. The denominator polynomial cannot be equal to zero. In this lesson we will look at the long range and short range behavior of rational functions.

Long Range Behavior

Asymptotes (Inspired by Analytic Geometry, Ross R. Middlemiss, McGraw-Hill Book Company, Inc, 1955)

We will define two polynomials that make up a fraction. The numerator polynomial will be N(x) and the denominator polynomial will be D(x).

Vertical Asymptotes: To find the vertical asymptotes set D(x) = 0 and solve for the values of x. The figure provides as example of this:

Horizontal Asymptotes: There are three possible cases

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