Rational Functions

1. What do you Mean by Rational Function?

Rational function is a type of function which is expressed as a fraction where both numerator and denominator must be a polynomial and the denominator is never equal to zero.

2. How to Simplify a Rational Function?

A rational function is simplified by factorising the numerator and denominator and then cancelling out the common factors.

3. What are Conditions for a Function to be a Rational Function?

A rational function may have a constant numerator and a polynomial denominator or both numerator and denominator as polynomials. A rational function can never have constant denominator.

4. Why are functions called rational functions?

Functions are called rational functions when they are expressed as a ratio of two polynomials. The term “rational” comes from “ratio,” as these functions represent the ratio of two integers.

5. What is a rational and irrational function?

Rational functions are expressions where one polynomial is divided by another, resulting in a finite, well-defined output. Irrational functions involve radicals.

6. What is Meant by Domain and Range of a Function?

Domain of the function is the set of all the numbers for which the function produces a finite value. Range is the set of all values that are obtained when putting the variable in function equal to any value from the domain.

7. What are Asymptote?

Asymptotes are imaginary lines that a curve approaches but never quite touches. They describe behavior like the curve getting closer to a limit without reaching it.

8. How is Vertical Asymptote Calculated?

Vertical Asymptote is calculated by simplifying the rational function first and then setting the denominator equal to zero and finding the value of the variable for which denominator becomes zero.

9. What is meant by Horizontal Asymptote of Rational Function?

A horizontal asymptote of a rational function is a line parallel to the x-axis and is of the form y=a where a is any number. This line appears to touch the graph of the rational function but it never touches it actually.

10. What is an Oblique Asymptote?

It is a slant line which appears to touch the graph of the rational function but never touches it. It is present only in the case where degree of numerator N = degree of denominator D+1.

11. What are Applications of Rational Functions?

Rational functions are used in various real life scenarios such as business, medical and science.

Rational Function is a type of function that is expressed as a fraction where both the numerator and denominator must be a polynomial and the denominator can never equal zero. Thus a rational function is similar to a fraction but the numerator and denominator are polynomial functions. In simple words, the rational function can be defined as the ratio of two polynomials. Rational functions find applications in various daily life problems and in various fields in life.

In this article, we shall discuss rational function in detail.