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

- anonymous

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- schrodinger

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- Mertsj

A function is a relation in which no two ordered pairs have the same first number.

- anonymous

Sorry, i'm having a hard time uploading photos. There are specific ones I don't get

- anonymous

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- anonymous

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- anonymous

is the first picture a function? I know the rest but not sure if they're one to one or not

- myininaya

the first picture is just a picture of one graph right?

- anonymous

yup!

- myininaya

Anyways have you ever heard of a vertical line test?

- anonymous

yeah, but i'm still not sure about that one :/

- myininaya

the holes you see there means the function isn't actually defined there
do you know that?

- anonymous

nope, i'm confused

- myininaya

for example:
|dw:1435801685311:dw|
f(1)=1

- myininaya

like f(1) is not assigned to 0

- anonymous

oh so does that mean it passes the vertical line test?

- myininaya

yep

- anonymous

ohh thanks! how do you tell if it's one to one?

- myininaya

there is a horizontal line test you can perform

- myininaya

if you draw a horizontal line
and more than one point lies on it then it is not one-to-one

- anonymous

wait so do i consider the points that aren't defined

- myininaya

you only considered things that are defined

- anonymous

is it one to one then because the other point isn't defined

- myininaya

|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|

- myininaya

no just so you know when you see a curve or a line you are actually seeing infinitely many points together

- myininaya

|dw:1435801941050:dw|

- anonymous

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?

- myininaya

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

- myininaya

well the second one is not even a function
do you know why?

- anonymous

yep doesn't pass the vertical line test

- myininaya

oh you mean

- myininaya

the second picture first graph sorry

- myininaya

anyways the first graph is a function because it passes the vertical line test
why do you say it is non one to one?

- anonymous

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

- myininaya

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

- anonymous

ok thanks! i think i got the hang of it. :)

- myininaya

cool stuff :)

- anonymous

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? ://

- anonymous

@myininaya

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