### Learning Outcomes

By the end of this section, you will be able to:

- Define a function using tables
- Define a function from a set of ordered pairs
- Define the domain and range of a function given as a table or a set of ordered pairs
- Write functions using algebraic notation
- Use the vertical line test to determine whether a graph represents a function
- Given a function described by an equation, find function values (outputs) for numerical inputs
- Given a function described by an equation, find function values (outputs) for variable inputs

In this module you will investigate the general characteristics of mathematical functions. Functions describe special relationships called *relations* between sets of items or values. This ability to describe well-defined relations is useful for making mathematical models to predict behavior or outcomes in certain situations.

Before diving into a detailed investigation of functions, though, it will be good to build up an intuitive understanding of what they are. In this reveiw section we’ll define what a function is and see the notation we use to write them. We’ll also get an introduction to how functions are evaluated and how they appear on a graph.

Warm up for this module by refreshing important concepts and skills you’ll need for success. As you study these review topics, recall that you can also return to Algebra Essentials any time you need to refresh the basics.

### Recall for success

Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.