Question

What is a function? Can the following sets of ordered pairs represent a functions? Why or Why not?

A= {(-4,-4), (2,0), (6,4) ,(10,2)} -
B ={(9,3), (9,-3), (4,2), (5,-2)}
C ={(-3,7), (-2,7), (-1,7),(0,7)}

Answer 1

Sets A and C represent functions, but Set B does not.

Explanation:

When you have ordered pairs such as those listed, you can immediately write out the domain in each case by writing out the set of first elements of the ordered pairs: In set A, the domain is {-4, 2, 6, 10}.

In set B, the domain is {9, 9, 4, 5}.

In set C, the domain is {-3, -2, -1 0}.

Rule: every first element of the domain must be unique (no two inputs are the same).

Looking at set A, we see that every first element is unique (no duplications here). Thus, set A represents a function.

Looking at set B, we see that there's one case of duplication: 9 appears twice as a first element of the given ordered pairs. Thus, set B does not represent a function.

Looking at set B, we we see that every first element is unique (no duplications here). Thus, set C represents a function.