Ratio of two polynomial Functions is defined as a rational Function, where, a Polynomial is a finite length expression, made up of 3 basic mathematical operations( addition, subtraction and multiplication and non-negative exponents) which contains variables and constants(like is a polynomial but is not a polynomial) . A function which evaluates a polynomial is known as polynomial function. One argument function named as g , is said to be polynomial if it satisfies ,
g(a) = yn an + yn-1an-1 + … + y2a2 + y1a + y0
Example : g(a) = a3 – a
The function 'a' is said to be rational function only if it can be written as,
g(a) = R(a) / S(a)
where R and S are polynomial Functions in a and S is not zero polynomial. The Set of all points ‘a’ for which the denominator S(a) is not zero comes under the Domain of g. One can assume that this rational function is written in its lowest degree i.e. R and S have many positive degree.
Polynomial functions with S(a) = 1, is said to be rational functions. Functions that can be written in this form are not rational functions.
Ex : g(a) = sin(a) , is not a rational function. It is not necessary that ‘a’ need to be variable.
Example: The rational function g(a) = is defined at a2 = 6 a = .
The rational function g(a) = (a2 + 3) / a2 + 1 can’t be defined for the complex numbers but can be defined for Real Numbers. If value of a is a Square root of -1then it Mean the evaluation leads to division by zero.
g(b) = (b2 + 2) / (b2 + 1) = (-1 + 3) /(-1 + 1) = 2/ 0, which is undefined.
Define Asymptotes of Rational Functions Coming soon.
We study different types of Functions in mathematics like quadratic, linear etc. and Rational Function is one of them. Here we will define rational function. A function that contains two Polynomials in fraction form or written in ratios is known as rational functions. Let's see mathematical representation of rational function. In case of polynomial with one vari...Read More
A function can be defined as term in mathematics which states relationships between constants and one or more variables. We do differentiation in order to reduce the equation with respect to a certain variable. Differentiating Functions with Real Numbers except for those involve finding Derivatives of rational functions or expressions including Fraction...Read More