Question

Which relation defined by a set of ordered pairs is a function?

1. {(6, 2), (6, 3), (5, 4), (6, 6), (7, 6)}


2. {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)}


3. {(–2, 6), (3, –6), (–4, 5), (6, –6), (6, –7)}


4. {(2, 6), (3, 6), (4, 5), (6, 6), (6, 7)}

Answer 1

The relation {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)} is a function ⇒ answer 2

Explanation:

- Relation is a set of inputs and outputs

- Function is a relation where each input has only one output

- Ex: The relation {(2 , 3) , (2 , 5) , (3 , 7)} is not a function because the

input 2 has two outputs 3 and 5

The relation {(-2 , 3) , (2 , 5) , (3 , 7)} is a function because each input

has only one output

* Let us solve the problem

- The first relation is :

{(6, 2), (6, 3), (5, 4), (6, 6), (7, 6)}

∵ The input 6 has three outputs 2 , 3 , 6

∴ The relation is not a function

- The second relation is :

{(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)}

∵ Each input has only one output

∴ The relation is a function

- The third relation is :

{(–2, 6), (3, –6), (–4, 5), (6, –6), (6, –7)}

∵ The input 6 has two outputs -6 , -7

∴ The relation is not a function

- The fourth relation is :

{(2, 6), (3, 6), (4, 5), (6, 6), (6, 7)}

∵ The input 6 has two outputs 6 , 7

∴ The relation is not a function

* The relation {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)} is a function