# Video: Defining Functions

Which of the following relations is a function?

01:18

### Video Transcript

Which of the following relations is a function?

For each of these relations, on the left of the inputs and on the right we have the outputs. A pairing of any set of inputs with there corresponding outputs is called a relation. While every function is a relation, not all relations are functions. So we have to decide which are functions.

To be a function, there needs to be exactly one output for every input. Imagine the inputs as π₯s and the output as π¦s. When we plug in a value for π₯, we should only get one answer for π¦. So for our first option, when we plug in π, we get one. And when we plug in π, we get three. That would represent a function.

For option π, if we would plug in, π we would get one. If we would plug in π, we would get two. But if we would plug in π, we would get two and we would get three. And it doesnβt make sense. When we plug in a value, we should get exactly one answer.

So this would not represent a function. And then option π would represent a function because when we plug in π, weβll get three. When we plug in π, we get one. And when we plug in π, we get three. Therefore, the relations that are functions are π and π.