Video: Determining Whether a Relation Represented by an Arrow Diagram Is a Function

Which of the following relations is a function? [A] Relation A [B] Relation B.

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Video Transcript

Which of the following relations is a function? Relation A or relation B.

Looking at each relation, the numbers on the left are the input values. These are the numbers that we would plug in. The numbers on the right are the output values. These would be our answers. So for example, looking at relation A, it says that if we’d plug in negative three, we would get an answer of positive three.

So how do we know if a relation is a function? In order to be a function, every input value, so all the numbers that we plug in, has exactly one output value. In summary, this means every number that we would plug in, we should get one answer. And that kinda makes sense. If you plug a number into an equation, you shouldn’t get one answer the first time you plug it in and then a different answer the next time you plug it in. You should only get one answer.

So let’s look at our relation A. As we’ve already seen, negative three gets us an answer of three. Negative two has one answer of negative six. If we plug in negative one, we get one answer. That’s zero. Plugging in zero, we get 15. And plugging in one, we get negative one. So every input value had exactly one output value. So relation A is a function.

Let’s go ahead and check relation B. All but one of the input values have exactly one output value. However, when we plug in one, we get an answer of zero and 15. And again, that does not make sense. So this would mean relation A is our function.

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