Rational Functions

Click here to open an associated Mathcad worksheet:

Graphic Representation

In the short term, rational graphs are recognized by there singularities and their roots. The number of these features is limited only by the degrees of the polynomials in the numerator and the denominator.

In the long term, rational graphs take on only three basic shapes. They either resemble an even power, an odd power, or they are asymptotic to a horizontal line:

The case depends entirely on the ratio of the terms of highest power in the numerator and the denominator.

The above graphs show just a few of the members of the family of rational functions. To see how these and other rational graphs can be created by tuning the family's parameters, see the associated worksheet.