Transcription
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 -1, 3. So that's the point (-1, 3). So, if we, if we assume that this is our x-axis and that that is our f(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 -1 into our function, or the thing that might be a function, or maybe our relation, you'll get a 3. So it's telling us that f(-1) is equal to 3. So, so far it could be a reasonable function: you give me -1, and I will map it to 3.
Then they have at: if x is 2, then our value is -2. This is the point (2, -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 -2. Seems fair enough. Let's see this next value here. This is the point (3, 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, let me do this in magenta. So what happens if I input 4 into my function? So this is f right here. Well, according to these points, there's two points that that relate to four that four can be mapped to. I could map it to the point (4, 5) up here. (4, 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'll, I could also give you a 1, cuz that's the (4, 1). So this is not a function. It can be a function if for some input into the function you could give me two different values, and you can see that right here. An easy test is to just see, look for one value; I have two points for this relation. So this cannot be a function. So this is not a function!