What is a rational function?

Answer 1

In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational numbers.

In the case of one variable, , a function is called a rational function if and only if it can be written in the form

where and are polynomial functions in and is not the zero polynomial. The domain of is the set of all points for which the denominator is not zero, where one assumes that the fraction is written in its lower degree terms, that is, and have several factors of the positive degree.

Every polynomial function is a rational function with . A function that cannot be written in this form (for example, ) is not a rational function (but the adjective "irrational" is not generally used for functions, but only for numbers).

An expression of the form is called a rational expression. The need not be a variable. In abstract algebra the is called an indeterminate.

A rational equation is an equation in which two rational expressions are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.