Question Video: Determining If a Relation Represented by an Arrow Diagram Is a Function Mathematics • 8th Grade

Does the relation shown by the arrow diagram represent a function?

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Video Transcript

Does the relation shown by the arrow diagram represent a function?

Before deciding if this is a function or not, let’s go ahead and take a closer look at the arrow diagram. On the left, we have our 𝑥-values, which would be the inputs — the numbers that we would plug in. And on the right, we have 𝑦. These would be our output values or the answers.

So this arrow diagram is showing if we plug in 16, we get 32. And if we plug in 16 again, we get 33. If we plug in 18, we get 34. And if we plug in 19, we get 35. So how will we know if this represents a function? In order to be a function, every input value — so every 𝑥-value — has exactly one output value.

Therefore, our answer is going to be no because of this instance by the 16. It’s saying if you’d take an equation and plug in 16, you would get an answer of 32. And then if you would plug it in again, you might get an answer 33.

And that doesn’t make sense. So this input value should have exactly one answer just like when we plug into an equation, we should get one answer. If we plug in again and get a different answer, that means we probably did something wrong on either the first or the second time. We would have to check again to find out. Therefore, again, this arrow diagram does not represent a function. So our final answer is no.