# Chapter 12: Rational Equations and Functions

**At Grade**Created by: CK-12

## Introduction

Fractional functions with a polynomial in the numerator and the denominator are known as rational functions. The graphs of these functions grow closer and closer to certain values without ever reaching those values. This is called asymptotic behavior. In this chapter, you’ll explore the asymptotes of rational functions. You’ll also perform operations on rational expressions and solve rational equations. In the real world, rational equations are often used to model electrical circuit and distance problems.

- 12.1.
## Inverse Variation Models

- 12.2.
## Graphs of Rational Functions

- 12.3.
## Horizontal and Vertical Asymptotes

- 12.4.
## Inverse Variation Problems

- 12.5.
## Division of Polynomials

- 12.6.
## Determining Asymptotes by Division

- 12.7.
## Excluded Values for Rational Expressions

- 12.8.
## Multiplication of Rational Expressions

- 12.9.
## Division of Rational Expressions

- 12.10.
## Addition and Subtraction of Rational Expressions

- 12.11.
## Applications of Adding and Subtracting Rational Expressions

- 12.12.
## Rational Equations Using Proportions

- 12.13.
## Applications Using Rational Equations

### Chapter Summary

## Summary

This chapter begins by distinguishing between three variation models: direct variation, inverse variation, and joint variation. It then moves on to graphing and solving rational functions, with particular attention paid to asymptotes. Next, it addresses simplifying rational expressions by factoring and dividing. The four mathematical operations of multiplication, division, addition, and subtraction are explored in the context of rational expressions. The chapter concludes with real-life applications of rational equations and methods for solving them.

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