Definition: Rational Functions

Definition 1: Gilbert, J. (1991). Guide to Mathematical Methods. Hampshire, England: Macmillan. (p. 9)

The general rational function, f, is defined by

    \[f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}\]

where p and q are both polynomials.  We must be careful to specify in the definition of f a domain which excludes values of x at which q\left(x\right) is zero.

Examples of rational functions are:

    \[f\left(x\right)=\frac{1}{x}\]

    \[f(x)=\frac{2x^2-3x+4}{x^3-1}\]

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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