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Testing if a relationship is a function

Learn to determine if points on a graph represent a function. Created by Sal Khan and Monterey Institute for Technology and Education.

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Video transcript

We're asked: Do the points on the graph below represent a function? So in order for the points to represent a function, for every input into our function, we can only get one value. So if we look here, they've graphed the point--it looks like negative 1, 3, so that's the point negative 1, 3. So if we assume that this is our x-axis and that is our f of x axis, and I'm just assuming it's a function, I don't know whether it really is just now, this point is telling us that if you put negative 1 into our function, or that thing that might be a function, or maybe our relation, you'll get a 3 So it's telling us that f of negative 1 is equal to 3. So far it could be a reasonable function. You give me negative 1 and I will map it to 3. Then they have if x is 2, then our value is negative 2. This is the point 2, negative 2, so that still seems consistent with being a function. If you pass me 2, I will map you or I will point you to negative 2. Seems fair enough. Let's see this next value here. This is the point 3 comma 2 right there. So once again, that says that, look, if you give me 3 into my function, into my black box, I will output a 2. Pretty reasonable. No reason why these points can't represent a function so far. Now, what about when we input 4 into the function? Let me do this in magenta. So what happens if I input 4 into my function? So this is 4 right here. Well, according to these points, there's two points that relate to 4 that 4 can be mapped to. I could map it to the point 4 comma 5. So that says if you give me a 4, I'll give you a 5. But it also says if you give me a 4, I could also give you a negative 1 because that's the point 4, negative 1 So this is not a function. It cannot be a function if for some input into the function you could give me two different values. And you can see that right here. And an easy test is to just see, look, for one value I have two points for this relationship. So this cannot be a function. So this is not a function! I'll put an exclamation mark.