有理函数是可以表示为以下形式的函数：

，不全为0。

有理数式是多项式除法的商，有时称为代数分数。

• 不失一般性可假设分子、分母互质。若存在，使得是分母的因子，则有理函数存在垂直渐近线。
• 若，有水平渐近线。
• 若，有水平渐近线。
• 若，有斜渐近线。

In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers, they may be taken in any field K. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero and the codomain is L.