# 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 𝑥s and the output as 𝑦s. When we plug in a value for 𝑥, we should only get one answer for 𝑦. So for our first option, when we plug in 𝑎, we get one. And when we plug in 𝑐, we get three. That would represent a function.

For option 𝑏, if we would plug in, 𝑎 we would get one. If we would plug in 𝑏, we would get two. But if we would plug in 𝑐, we would get two and we would get three. And it doesn’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 𝑐 would represent a function because when we plug in 𝑎, we’ll get three. When we plug in 𝑏, we get one. And when we plug in 𝑐, we get three. Therefore, the relations that are functions are 𝑎 and 𝑐.