Can someone please help me with this math question? Please? I'll fan and give a medal!!

Question

abbycross167 · Answer

Use the set {(1, 0), (2, 1), (3, 0), (4,2)} for numbers 1 - 3
1.	Is the relation a function, why or why not?

abbycross167 · Answer

@Abbles do you think you could try to help me?

abbles · Answer

It can only be a function if there is only one y value for each x value.  Are you familiar with the vertical line test?

abbles · Answer

Correction: There can only be one X value for every y value.  Meaning, you can't have a point at (2, 4) and a point at (2, 6), since they have the same x value.

abbycross167 · Answer

I'm somewhat familiar with the vertical line test

abbles · Answer

Okay.  So you know that if you plot the points and draw vertical lines on the graph, two points cannot intersect the same vertical line (they would have the same x value)... if that makes sense.

abbles · Answer

Do any of your points have the same x coordinate?

abbycross167 · Answer

so this would be a function because none of them have the same x coordinate?

abbles · Answer

Correct.  There can be two points with the same y-coordinate, but not the same x-coordinate.

abbles · Answer

Because if two points had the same x-coordinate, they would form a vertical line.

abbles · Answer

http://www.wolframalpha.com/input/?i=plot+(2,+4)+and+(2,+7) That is point (2, 4) and (2, 7) plotted for you to see. It makes a vertical line.

abbycross167 · Answer

so the points (2, 4) and (2, 7) are not a function  because they have the same x value?

abbycross167 · Answer

@Abbles

abbles · Answer

Right.

abbles · Answer

Your relation, however, is a function.  Just as you said.

abbles · Answer

What is question #2?

abbycross167 · Answer

this is question 2
2.	State the inverse of each relation.

abbles · Answer

To find the inverse relation, simply swap the x and y values of each coordinate.
For example, if the original function had point (5, 7) then the point would become (7, 5) when inversed.

abbles · Answer

Do that with all of the points in the relation.

abbycross167 · Answer

{(1, 0), (2, 1), (3, 0), (4,2)} 
=
(0,1) (1,2) (0,3) (2,4)
like this?

abbles · Answer

Perfect!

abbycross167 · Answer

then what? or is that all?

abbles · Answer

You could write it f^-1(x) and then state all your values in brackets {like this}

abbles · Answer

Otherwise, your good!  You have the inverse function.

abbycross167 · Answer

So like this?
f^-1(0,1)

abbles · Answer

And list the rest of the coordinates.  There are a few different ways to write functions (you could use f(x) or y or other variables) but you should be good.

abbycross167 · Answer

So do the rest of the coordinates like that?
f^-1(0,1)
f^-1(1,2)
f^-1(0,3)
f^-1(2,4)

abbycross167 · Answer

@Abbles

abbles · Answer

No no, it should be all in one function.  Like this:
f^-1: {(0, 1), (1, 2), (0, 3), (2,4) etc.}

But it really depends on how the original function was written.  Was it f(x)?  Or y = ... ?

The above should work.  Or just like the coordinates inside of a set of brackets:
{(0, 1), (1, 2), (0, 3), (2,4) etc.}
^That way might be best in your situation.

abbles · Answer

@abbycross167  Still with me?

abbycross167 · Answer

yes sorry, my WiFi messed up

abbycross167 · Answer

this is the 3rd question-
Is the inverse a function, why or why not?

abbycross167 · Answer

it won't be a function because (0,1)(0,3) have the same x coordinate. Right?
@Abbles

abbles · Answer

Exactly!  You are right.

So I would list the inverse function inside brackets {0,1) etc. } instead of using the negative inverse function notation f^-1(x).. since it is not, in fact, a function.  :)