## Introduction

Up until this point, you’ve dealt with non-fractional polynomials, but what if you were asked to solve a fractional function with a polynomial in the numerator and the denominator? Such functions 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 find 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.

## Chapter Outline

- 12.1. Inverse Variation Models
- 12.2. Graphs of Rational Functions
- 12.3. Horizontal and Vertical Asymptotes
- 12.4. Determining Asymptotes by Division
- 12.5. Division of Polynomials
- 12.6. Inverse Variation Problems
- 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 then performed on rational expressions. The chapter concludes with real-life applications of rational equations and methods for solving them.