Rational Function


Rational Function can be described as ratio of two polynomial functions or we can say that when we divide a polynomial function by another polynomial function then it will be called as rational function. We can describe a rational functions as:

r(x) = p(x) / q(x).

Here p(x) and q(x) are two polynomials. In this p(x) is called as numerator and q(x) is called as denominator.

It is not necessary for coefficient to be a rational number. In rational function q(x) can never be zero because it will convert into infinity which is not defined. In rational function terms p(x) and q(x) shares some common fractions with each other.

In mathematics every polynomial function is assumed as rational function which has q (x) = 1.

Here p(x) / q(x) is called as rational expression, where 'x' must be a variable that behaves as indeterminate. Rational equation is an equation in which two rational expressions are set to equals to each other. We can solve the rational expressions by applying cross multiplication. In rational function also division by zero is undefined.

For example f(x) = (x2 + 2) / (x2 – 1) is also a rational function where (x2 + 2) is numerator and (x2 - 1) is denominator.

Here domain of rational function f(x) will contain all values of 'x' where q(x) is non- zero. Let us take an example to understand it.

F(x) = (x + 3) / (x – 1),

Here domain of function will not contain value x = 1 because it will make (x - 1) = 0, which is undefined.

Topics Covered in Rational Function

Asymptotes of Rational Functions

If n (y) and d (y) are two polynomial functions then ratio of these two polynomials will give rational function. That is rational function is a quotient of n (y) and d (y) polynomials. Mathematically,


r = n (y) / d (y), here d (y) ≠ 0.


Rational function will have a y - intercept ('x' will equals 0) only if numerator n (y) =...Read More

Math Topics