# Relations and Functions

Many things in the world around us can be described in terms of **relationships** and **functions** that operate on **inputs **to give meaningful **outputs**. The set of inputs is called the **domain **and the set of ouputs is called the **range **of the underlying relationship/function. Many complex objects are the "sum" of individual basic components. It is possible to understand how such complex objects work by understanding how the individual components work.

In this module we will learn about mathematical functions that form the foundation of calculus. The discussion centers around what a function is made of, how it operates, and its applications. By the end of this module, you should be able to

- Identify domain and range of a function
- Describe and notate a function using letters
- Evaluate a function
- Find the average rate of change in the value of a function with respect to changes in input values
- Find the difference quotient
- Graph a function or a relationship
- Perform
**Vertical Line Test**to tell if a graph represents a relationship or a function. - Study
**transformations of functions**