Is relation t a function? Is the inverse of relations t a function?
Relation t
x 0 2 4 6
y -8 -7 -4 -4

- anonymous

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- anonymous

A. Relation t is a function. The inverse of relation t is not a functions.
B. Relation t is not a function. The inverse of relation t is a function.
C.
Relation t is not a function. The inverse of relation t is not a function.

- anonymous

@UsukiDoll

- UsukiDoll

ok so to determine a function we use the vertical line test for a graph. Similarly we use
a horizontal line test for a graph to determine a one to one function.
but this time we don't have a graph. Instead we have a chart.
This may be a while back since I've last did charts though
If I remembered correctly the function must have the x not repeating and the one to one function (inverse) must have the y not repeating

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## More answers

- anonymous

So A?

- UsukiDoll

yeah... I'm still trying to remember though... this was way back in 2008 when I did this.

- anonymous

Any help is better than no help

- UsukiDoll

ok... now I got my memory back after I read a paragraph somewhere .. we can't have duplicates for x or y

- anonymous

So the answer is still A, correct?

- UsukiDoll

there's an example in my book somewhere.. I have to find it before giving out an answer.

- anonymous

ok, ill wait

- UsukiDoll

ok that was mapping and proofs. It's too strong for this problem... but I do know that we can't have anything repeating

- anonymous

Im gonna go with A than because the top row isn't repeating

- UsukiDoll

the original function has a repeated value for y though..

- anonymous

So c?

- Astrophysics

Well for it to be a one - to - one function the x and y values are to be used only once. So if you can switch the x and y variables around to create a inverse relation, we would notice function t would not be a one - to - one function since there are two of the same y values, then we can conclude the inverse is not a function.

- UsukiDoll

if we switch.. that would mean that there exists x values that are repeating.

- anonymous

So it's C @Astrophysics

- UsukiDoll

Ok I'm seeing this horizontally .. I'm going to draw vertical |dw:1435810073365:dw|

- UsukiDoll

alright so there are repeats.. since we can't have that.. it's not a function .

- UsukiDoll

so switching to grab the inverse
|dw:1435810139494:dw| same problem occurs

- UsukiDoll

Since we have repetitions or duplicates of x-values with different y-values, then this relation ceases to be a function.

- Astrophysics

Well lets put it like this, |dw:1435810074921:dw| it is not a function since the x value of -4 now has two different y values, so it's not a function, I hope that makes sense

- Astrophysics

yeah exactly

- anonymous

So the answer is C correct?

- anonymous

Since if it gets reversed than there would be duplicates on x and y

- anonymous

@Astrophysics

- UsukiDoll

if it's reversed we have duplicate x values
if it's not reversed we have duplicate y values. either way it's not a function since each number has to be unique

- Astrophysics

Yeah, that sounds good to me, since it's not 1 - to - 1.

- anonymous

I have another question

- Astrophysics

Note that for a 1 - to - 1 function it has to pass both vertical and horizontal line test.

- UsukiDoll

no... 1 to 1 is horizontal line test only

- anonymous

What is the inverse of the given function?
y = 7x^2 - 3.

- UsukiDoll

for graphs

- UsukiDoll

ok first switch the x and y

- UsukiDoll

for y=7x^2-3

- Astrophysics

I just googled it to make sure and look |dw:1435810563144:dw|

- anonymous

so make it x=7y^2-3

- UsukiDoll

yes now solve for y

- anonymous

I wish i was as good at math as you guys are

- UsukiDoll

If no horizontal line intersects the graph of the function more than once, then the function is one-to-one.

- UsukiDoll

:P

- UsukiDoll

\[x=7y^2-3\]
k now solve for y

- UsukiDoll

so we need y by itself

- anonymous

So how do i factor it to itself?

- anonymous

7*7=49
49-3=46

- UsukiDoll

whoa.

- anonymous

Am i totally off

- UsukiDoll

you want the inverse of the function. This has nothing to do with factoring

- anonymous

So how do i do an inverse?

- Astrophysics

Oh okkkk yes, I understand @UsukiDoll I get what you mean now haha, I kept saying it has to be 1 to 1 for it to pass both, but it just needs to pass horizontal for it to be 1 to 1 and if it passes a vertical line test it is just a function! :) Ok now I'll let you do your thing!

- UsukiDoll

we were on the right track
so our original equation
y=7x^2-3
we switch the x and y
x=7y^2-3
now we need to solve for y

- UsukiDoll

to have y by itself we need to ______ 3 to both sides

- anonymous

add

- anonymous

\[y \pm \sqrt{\frac{ 3+x }{ 7}}\]

- UsukiDoll

x+3=7y^2
\[\frac{x+3}{7}=y^2 \rightarrow \sqrt{\frac{x+3}{7}}, -\sqrt{\frac{x+3}{7}}\]
my x is in a different place but it wouldn't matter since the answer is the same

- anonymous

yay we figured it out! *high five*

- UsukiDoll

yay :D *high fives*

- anonymous

haha

- anonymous

It's a function if we assume \(\{0,2,4,6\}\) is the domain

- Hero

For the original question posted, I don't agree with "C" as an answer.

- anonymous

How come @Hero

- Astrophysics

I don't either actually, because I kept saying 1 to 1 function, that is true it's not a 1 to 1 function, but however it is a function as the x does not repeat itself.

- Hero

Plot each point, then perform a vertical line test:
https://www.desmos.com/calculator/ogb1oqtoi2

- anonymous

So i was right when i said it is A?

- Astrophysics

That seems better

- anonymous

It's A

- Hero

A is correct.

- Astrophysics

Sorry for the confusion @EllenJaz17 :P

- anonymous

Thanks guys!

- anonymous

No problem, at least im learning

- anonymous

A function is:
Left total - all elements in the domain used at least once.
Many to One - all elements in the domain used no more than once.

- UsukiDoll

thanks for the memory refresher x never had repeats for the function , but switch x and y and now there are repeats

- anonymous

Mono, did you draw that avatar?

- UsukiDoll

no...

- Astrophysics

Haha

- UsukiDoll

yeah it was A for that question

- UsukiDoll

but like I said I've done this way back . so it's not 100% until @wio showed up and I saw what he was talking about.

- UsukiDoll

then it popped back into my mind... there's a bunch of Math topics that don't appear any more when you study further

- Astrophysics

Yeah it was a good review, I think last time I did a problem like this was in middle school

- UsukiDoll

the graph versions.. those were the ones I knew and functions... well my book had a strong approach to it... it was about mapping... surjection/injection bijection so I highly doubt it would be used.

- anonymous

For the function f(x) = (8-2x)2 ,find f-1 . Determine whether f-1 is a function.

- anonymous

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