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) }

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

Step-by-step 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