1
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2
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We're asked: Do the points on the graph

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below represent a function?

4
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So in order for the points to represent a function, for

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every input into our function, we can only get one value.

6
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So if we look here, they've graphed the point--it looks

7
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like negative 1, 3, so that's the point negative 1, 3.

8
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So if we assume that this is our x-axis and that is our f

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of x axis, and I'm just assuming it's a function, I

10
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don't know whether it really is just now, this point is

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telling us that if you put negative 1 into our function,

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or that thing that might be a function, or maybe our

13
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relation, you'll get a 3 So it's telling us that f of

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negative 1 is equal to 3.

15
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So far it could be a reasonable function.

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You give me negative 1 and I will map it to 3.

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Then they have if x is 2, then our value is negative 2.

18
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This is the point 2, negative 2, so that still seems

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consistent with being a function.

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If you pass me 2, I will map you or I will point you to

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negative 2.

22
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Seems fair enough.

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Let's see this next value here.

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This is the point 3 comma 2 right there.

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So once again, that says that, look, if you give me 3 into my

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function, into my black box, I will output a 2.

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Pretty reasonable.

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No reason why these points can't represent

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a function so far.

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Now, what about when we input 4 into the function?

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Let me do this in magenta.

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So what happens if I input 4 into my function?

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So this is 4 right here.

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Well, according to these points, there's two points

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that relate to 4 that 4 can be mapped to.

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I could map it to the point 4 comma 5.

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So that says if you give me a 4, I'll give you a 5.

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But it also says if you give me a 4, I could also give you

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a negative 1 because that's the point 4, negative 1 So

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this is not a function.

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It cannot be a function if for some input into the function

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you could give me two different values.

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And you can see that right here.

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And an easy test is to just see, look, for one value I

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have two points for this relationship.

46
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So this cannot be a function.

47
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So this is not a function!

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I'll put an exclamation mark.