**Chapter 4Relations and Functions**

4.1 Definitions

4.2 Function Notation

4.3 Piecewise Functions

4.4 Parent Functions and Transformations

4.5 Algebra of Functions

4.6 Inverse Functions

**4.1 Definitions**

In the first three chapters, you solved and graphed equations. Those equations, along with any set of ordered pairs, can be classified as relations. Some relations are also functions.

**Relation**

A *relation* is a set of input and output values. Relations might be shown as a set of ordered pairs, a mapping diagram, a graph, or an equation. Figure 4.1 shows five examples of relations. Relation (b) is a mapping diagram that shows the inputs in the left column and the outputs in the right column, and represents the ordered pairs (–3, 0), (2, 1), (4, 2) and ...