### Unit 6: Rational Functions

In this unit, you will apply what you have learned about functions to rational functions. Rational functions are based on the toolkit reciprocal functions and have many interesting characteristics. You will apply similar skills and techniques for defining intercepts and end behavior of polynomial functions to rational functions. By the end of this unit, you will be proficient in defining the local behavior and end behavior of a polynomial function and drawing the graph of a polynomial function given its characteristics.

**Completing this unit should take you approximately 2 hours.**

Upon successful completion of this unit, you will be able to:

- illustrate the properties of rational functions, including long-run behavior and local behaviors using arrow notation;
- identify vertical, horizontal, and slant asymptotes of rational functions given a graph or an equation;
- describe the domain of a rational function using standard notation given an equation or a graph;
- identify and graph removable discontinuities and intercepts of a rational function given an equation; and
- construct a graph or an equation of a rational function using its properties.

### 6.1: Characteristics of Rational Functions

In the first section on rational functions, you will learn about their general characteristics and how to use standard notation to describe them. When you are finished, you will be able to use arrow notation to describe long-run behavior given a graph or an equation. You will also be able to use standard notation to describe local behavior.

Domain and range are essential for rational functions since some inputs make them undefined. It is crucial to understand how to define the domain and range of rational functions because it allows you to determine asymptotes and the long-run behavior of rational functions.

In this section, you will use many of the same tools you used to find zeros of polynomials to find the zeros of rational functions. Finding the zeros (intercepts) will help you graph rational functions without a calculator.

### 6.2: Finding Asymptotes of Rational Functions

This section will dive deeper into the analytic and algebraic tools for finding the three types of asymptotes found in rational functions. Defining asymptotes will help you graph rational functions without a calculator, determine where the function is undefined, and give you a picture of the general behavior of the function.

### 6.3: Graphs and Equations of Rational Functions

In our final section on rational functions, we will bring all the skills we have learned together to draw graphs of ration functions without the help of a calculator. We will use asymptotes, intercepts, and general characteristics of the function in question. You will also be able to determine the equation of a rational function given a graph.