Rational Function
Previously we have discussed about real numbers definition and In today's session we are going to discuss about Rational Function, Ratio of two polynomial functions is known as the rational function. A rational function F(a) can be given as-
F (a) = p (a) / q (a), where ‘a’ is the variable on which function depends.
In the above function ‘p’ and ‘q’ are two polynomial functions and it should be noted that value of q ( a ) should never be zero. Here the function ‘f’ is defined as the domain of sets of all points ‘a’ for that, denominator q (a) will never be zero.
Keep in mind that every polynomial function is a rational function if q( a ) =1. Suppose we have a function written as f ( a ) = cos ( a ), then it is not a rational function .
So a rational function or a rational expression is defined in the form p (a) / q (a) here ‘a’ is not a variable but it is an indeterminate in the abstract algebra. Same rules of fraction also apply on the rational equation .We can understand the rational expression by rational function examples.
Some examples for defining the rational expression are as follows:
Here is a rational function f (a) = (a 3 – 2 a) / 2 ( a 2 – 5 ) but it is clear that for value a2 = 5, function is not rational.
Another example f ( a ) = (a 2 + 2) / (x 2 + 1) is a rational function for all real numbers but keep in mind that it is not a rational function for complex numbers .
In the next session we are going to discuss about Limits of sequence and function and You can visit our website for getting information about math tutor online and icse class 10 syllabus.