# Chapter 2: Analyzing Polynomial and Rational Functions

Difficulty Level:

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

## Introduction

In this section, you will be exploring different methods of using functions to identify specific solution sets. By evaluating graphs, expressions, and equations of different types, you will learn to glean important information from all kinds of situations. Specific topics covered in this section include:

- Functions with squared terms (quadratic functions)
- Polynomials with powers greater than 2
- Rational functions (functions involving polynomial division)
- Inequalities (greater-than / less-than)
- Polynomial division (both long division and synthetic division)
- Solving polynomial equations

Chapter Outline

- 2.1.
## Methods for Solving Quadratic Functions

- 2.2.
## Graphs of Quadratic Functions

- 2.3.
## Graphs of Polynomials Using Transformations

- 2.4.
## Graphs of Polynomials Using Zeros

- 2.5.
## Horizontal and Vertical Asymptotes

- 2.6.
## Oblique Asymptotes

- 2.7.
## Graphs of Rational Functions

- 2.8.
## Analysis of Rational Functions

- 2.9.
## Quadratic Inequalities

- 2.10.
## Polynomial and Rational Inequalities

- 2.11.
## Synthetic Division of Polynomials

- 2.12.
## Real Zeros of Polynomials

- 2.13.
## Intermediate Value Theorem

- 2.14.
## Fundamental Theorem of Algebra

### Chapter Summary

## Summary

This section focuses primarily on quadratic and rational functions, and presents multiple methods for solving and manipulating each. Lessons review and apply the concepts of asymptotes, including oblique or slant asymptotes, quadratic inequalities, synthetic division, and approximating real zeroes. This chapter culminates in an introduction to the Fundamental Theorem of Algebra.

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Description

This chapter focuses on concepts and skills relevant to solving problems involving polynomial and rational functions. Analytical, graphical and numerical methods are considered for solving polynomial and rational equations.

Difficulty Level:

At Grade
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Subjects:

Date Created:

Nov 01, 2012
Last Modified:

Mar 23, 2016
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