## 4-2 Relations and Functions

Objectives: Identify functions & find the domain and range of relations and functions.

Relationship is math can be represented in numerous ways. In 4-1, they were represented by graphs. In this section, they will be represented by a

**. A relation is a set of ordered pairs. They can be shown in various ways.**__relation__The ordered pairs for this mapping would be (8, -1), (9, -3),

(10, -1), & (13, 5).

The ordered pairs for this table would be (-3, 0), (0, 3), (3, 6), & (6, 9).

The

**of a relation is the (first) x-values (independent). The**__domain__**of a relation is the (second) y-values (dependent).**__range__The relation is the blue line segment.

The green represents the domain of the relation.

The red represents the range of the relation.

The green represents the domain of the relation.

The red represents the range of the relation.

The domain and range can be listed using inequalities or individual numbers, depending on how the relation is provided. See the example below.

The domain for this relation/mapping would be written:

The range for this relation/mapping would be written:

**D: {8, 9, 10, 13}**The range for this relation/mapping would be written:

**R:{-1, -3, 5}******Notice the braces before AND after.****A

*is a special type of relation that pairs each domain value with*__function__**EXACTLY**one range value.*To think of it another way, think of x as people and y as a place. A person, x, cannot be in more than one place, y, at a time, however, more than one person can be at the same place.*A function as a mapping, each x-value can have only ONE arrow to a y value. (The y values don't matter.) The above represents a function, even though two separate x values are sharing a y value (two people in one place). How about the mapping on the right?

To tell whether a relation is a function from a graph, you can simply use the VERTICAL LINE TEST. If a vertical line passes through more than one point of the graph, it is not a function. (Remember vertical goes up and down.)