What Is A Rational Function?

A rational function is defined as a ratio of two polynomial functions, with its denominator not equal to zero.

Domain Of Rational Functions

The domain of a rational function is defined by the values of the variable that do not make the denominator equal to zero.

Simplifying Rational Expressions

This section provides a detailed methodology for simplifying rational expressions by factoring and canceling common factors.

Vertical And Horizontal Asymptotes

This section discusses vertical and horizontal asymptotes of rational functions, explaining how they are determined based on the function's equation and its polynomial degree.

Vertical Asymptotes

Vertical asymptotes occur at values of x that make the denominator of a rational function equal to zero after simplification.

Horizontal Asymptotes

This section introduces horizontal asymptotes in rational functions, detailing their significance based on polynomial degrees.

Holes In The Graph

Holes in the graph of rational functions occur when a factor in the denominator cancels with a factor in the numerator.

Intercepts

This section describes how to find the x-intercept and y-intercept of rational functions.

X-Intercept

The x-intercept of a function is found by setting the function equal to zero and solving for x.

Y-Intercept

The y-intercept of a function is the point where the graph intersects the y-axis, found by evaluating the function at x=0.

Graphing Rational Functions

This section covers how to graph rational functions, focusing on essential components such as domain, asymptotes, and intercepts.

Solving Rational Equations

This section focuses on solving equations that involve rational expressions, guiding through the identification of restrictions, the use of least common denominators, and verifying solutions.

Summary

This section encapsulates the key concepts associated with rational functions, including their definitions, domains, simplifications, asymptotes, and graphing techniques.