Table of Contents
Explain in Detail :Rational Function Definition:
A rational function is a function that can be expressed as the quotient of two polynomial functions. The polynomial functions on the left and right hand sides of the equation are called the numerator and denominator, respectively. The rational function can be written in the form:, where and are real numbers and is a polynomial.
Rational Function Formula
A rational function is a function that can be expressed in the form of a quotient of two polynomials. The denominator polynomial is always a degree lower than the numerator polynomial. The function can be graphed by plotting the points given by the equation and connecting the points with a smooth curve..
Graphing Rational Functions
In this lesson, we will learn how to graph rational functions.
A rational function is a function that can be expressed as the quotient of two polynomial functions. The denominator of a rational function is always a polynomial function.
To graph a rational function, we first need to find the zeros of the function. The zeros of a rational function are the points where the function crosses the x-axis.
Next, we need to plot these points and then connect them with a line.
Types of Rational Functions
There are three main types of rational functions: polynomial, exponential, and logarithmic.
Polynomial rational functions are the simplest type of rational function. They are simply functions of the form, where P(x) is a polynomial.
Exponential rational functions are those of the form, where A is an positive real number and x is a real number.
Logarithmic rational functions are those of the form, where B is a positive real number and x is a real number.
Conditions For Graphing Rational Functions
The domain of a rational function is all real numbers.
The range of a rational function is all real numbers.
The y-intercept of a rational function is the value of y when x = 0.
The slope of a rational function is the coefficient of x in the function.
