Topic: Polynomial and Rational Functions

Subtopic: Rational Functions & Graphs

**Overview**

In this lesson we study the graphs of rational functions. __Rational functions__ are fractions with a polynomial in each of the numerator and the denominator. Their graphs have special features such as asymptote lines and holes (missing points). Our goal is to algebraically find these features from the function and then put the information together to produce the graph by hand.

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 3.5.1 Given a rational function algebraically find domain, intercept points, and missing points
- 3.5.2 Given a rational function algebraically find vertical, horizontal, and oblique asymptote lines
- 3.5.3 Use information obtained (points, asymptotes, etc.) about a rational function to produce it's graph by hand
- 3.5.4 Using a grapher, produce the graph of a given rational function and find its domain, intercept points, missing points, and asymptote lines
- 3.5.5 Find the rational function that would produce a given graph (i.e. from graph to function)

**Terminology**

Define: rational function, missing points, asymptote line (vertical, horizontal, and oblique)

**Supplementary Resources (recommended)**

Prof. Hoover's Review of Rational Functions and Asymptotes provides a comprehensive overview of the formulas and processes for algebraically finding the key features of the graph of a rational function.

**Supplemental Resources (optional)**

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics:

"Determining Key Components of Rational Functions"

"Graphing Rational Functions"

"Determining Equations of Rational Functions"