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# Testing if a relationship is a function

CCSS.Math:

## Video transcript

we are 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 looks like negative 1/3 so that's the point negative 1/3 so if we if we assume that this is our x-axis and that that is our f of X axis and I'm just assuming it's a function I don't know what 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 so far it could be a reasonable function you give me negative 1 and I will map it to 3 then they have at 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 to 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 a new special 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 that relate to for that 4 can be mapped to I could map it to the point 4 comma that's 5 up here 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 now 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 2 different values and you can see that right here in an easy test is to just see look for one value I have two points for this relation so this can not be a function so this is not a function I'll put an exclamation mark