please help :) Function or not a function? one to one or many to one? please explain! Pictures attached.

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please help :) Function or not a function? one to one or many to one? please explain! Pictures attached.

Mathematics
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A function is a relation in which no two ordered pairs have the same first number.
Sorry, i'm having a hard time uploading photos. There are specific ones I don't get
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is the first picture a function? I know the rest but not sure if they're one to one or not
the first picture is just a picture of one graph right?
yup!
Anyways have you ever heard of a vertical line test?
yeah, but i'm still not sure about that one :/
the holes you see there means the function isn't actually defined there do you know that?
nope, i'm confused
for example: |dw:1435801685311:dw| f(1)=1
like f(1) is not assigned to 0
oh so does that mean it passes the vertical line test?
yep
ohh thanks! how do you tell if it's one to one?
there is a horizontal line test you can perform
if you draw a horizontal line and more than one point lies on it then it is not one-to-one
wait so do i consider the points that aren't defined
you only considered things that are defined
is it one to one then because the other point isn't defined
|dw:1435801820547:dw| back to my picture again this function is not one-to-one because you have both f(1/2)=0 and f(0)=0 so for example on the imaginary horizontal line y=0 we see that more than one point lies it |dw:1435801903911:dw|
no just so you know when you see a curve or a line you are actually seeing infinitely many points together
|dw:1435801941050:dw|
oh!! i get it now. thanks! so the second picture, first one is not one to one right? and the circle graph isn't too? but the third (line) is?
we could also looked at the other line segment I drew but we only need one example to tell us that the function is not one-to-one
well the second one is not even a function do you know why?
yep doesn't pass the vertical line test
oh you mean
the second picture first graph sorry
anyways the first graph is a function because it passes the vertical line test why do you say it is non one to one?
idk i think it is because there is like a straight line on the x axis in the middle? so it doesn't pass the test or is that wrong
ok I thought that graph was basically of f(x)=x^3 which looks like this: |dw:1435802164888:dw| which is one-to-one but I'm having a little trouble reading that graph if that graph is really: |dw:1435802205725:dw| then yeah it isn't one to one
ok thanks! i think i got the hang of it. :)
cool stuff :)
wait I just took a test and it had a problem with the second graph you drew. I put it wasn't one to one and it was incorrect? ://

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