195

19

Basic Function Concepts

Representations of a Function

Basic function concepts are presented in this chapter. One of the fundamen-

tal concepts of mathematics is the notion of a function. In algebra, you will

see this idea in various settings, and you should become familiar with the

different representations (forms) of a function. Three of the most frequently

used representations are presented here.

Form 1: Ordered Pairs

A function is a set of ordered pairs such that no two different ordered pairs

have the same fi rst coordinate. The domain of a function is the set of all fi rst

coordinates of the ordered pairs in the function. The range of a function is

the set of all second coordinates of the ordered pairs in the function.

Problem Determine which of the two sets is a function and identify the

domain and range of the function.

f = {(4, 1), (3, 7), (2, 5), (5, 5)} w = {(5, 1), (4, 3), (6, 3), (4, 2)}

Solution

Step 1. Analyze the sets for ordered pairs that satisfy the function criteria.

Set f is a function because no ordered pairs have the same fi rst coor-

dinate. Set w is not a function because (4, 3) and (4, 2) have the same

fi rst coordinate, but different second coordinates.