Warm Up

 

A. Representing Relations

Relations connect two values that are related to one another. In mathematics, relations are defined as any set of ordered pairs. An ordered pair can be represented in different forms. Some examples of ordered pairs are shown in the chart.

Relation
a set of ordered pairs that can be represented in many ways

Representation
Form

Examples
List of ordered pairs
{(3, −10), (5, −9), (−14, −5), (2,15)}
Mapping Diagram
Table of Values
x
y
3
−10
5
−9
−14
−5
2
15
Graph

 

Example 1

Five friends discussed how many pairs of shoes they each own. They represented the results of the discussion in the mapping diagram shown. Represent the resulting relation as a set of ordered pairs.

When numbers are listed in a mapping diagram, it is common practice to list the numbers from least to greatest.

{(Bill, 3), (Sam, 5), (Jill, 14), (Sue, 18), (Amy, 25)}


A graph can also be used to represent a relation. Interpreting a graph is often more efficient than reading a list or table of values. The graph of a relation summarizes how two variables vary in relation to one another.

Graph
a visual depiction of the relationship between two variables