Which of the following rules represents a function?

eddy2017 said:
1=y^2
sub y^2 from both sides
1-y^2=y^2-y^2
switch terms
-y^2 +1=0 ----------sub 1 from both sides
-y^2 +1 -1 = 0-1
-y^2=-1 --------------diivide both sides by -1
-y^2/-1= -1/-1
y^2=1------------------taking square root of both sides
Click to expand...
What are you doing? You started with 1=y^2 and ended with y^2 = 1.
This tells me that you do not know what an equal sign means! Actually that does not surprise me as you use equal signs even when things are not equal.

You need to understand that if a=b, then b=a. That 8=x means x=8. You do not have to do anything to go from 8=x to x=8.

If 1=y^2, then y^2=1 !!!!!!!
 
eddy2017 said:
I understand now. I was not getting how to perform the substitution and check. That was what was throwing me off. When it comes to me it is not a question of being lazy it is a question that somehow I am not understanding the process.
I am gonna prove now that y^2=x^2 is not a function.
A) y^2 = x^2
If x=1 for example, how many different values for y?
pluggin' in the value
1^2=y^2
1=y^2
sub y^2 from both sides
1-y^2=y^2-y^2
switch terms
-y^2 +1=0 ----------sub 1 from both sides
-y^2 +1 -1 = 0-1
-y^2=-1 --------------diivide both sides by -1
-y^2/-1= -1/-1
y^2=1------------------taking square root of both sides
√y^2= √1
y=±√1
y=1 or y=−1
When x=1 I have two different values of y, then it is not a function.
I had to actually perform the entire operation to get it. Now I see why, honestly. I was not getting it until i did all this.

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when x=1
y=x^2.
y=1 ( there is only value for y, so it is a function)

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D) y^2 = x
If you randomly pick some value for x, then how many different values might there be for y?
let's say x=2
so,
y2=2 ---------Taking the square root

√y^2 = √2
y=+-√2
y=+-√2
y can be either y= +√2 , or -√2.

this one can not be a function either because there are two values for y
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|y|= x^2.
if you square some number, how many different values might y be?
let's say x=2

|y| = 2^2
|y| = 4
now apply the definition of absolute value, then
y=4
y=-4

it can not be a function either because y has two values.

I saw the by actually performing the operations it came alive for me.
Than you. if you can rectify something or confirm this I'd appreciate it.


it can not be a function here because the
Click to expand...
If you picked x=0, then is y^2=x^2 a function?
Note that, y^2 = 0^2 = 0, so y=0. One input--one output.
 
Jomo said:
If you picked x=0, then is y^2=x^2 a function?
Note that, y^2 = 0^2 = 0, so y=0. One input--one output.
Click to expand...
Yes, I think so. I think it is a function because I can get two values that are totaly valid and make a cvalid ordered pair (0,0)
y^2 =0^2 -------taking the square root
√y^2=√0^2
y=∓ 0

y= 0
y-0
getting the ordered pair (0,0) [Note: Zero, 0, is neither a positive nor a negative number, since it is neither greater nor less than itself].

It is a function! :)
 
eddy2017 said:
Yes, I think so. I think it is a function because I can get two values that are totaly valid and make a cvalid ordered pair (0,0)
y^2 =0^2 -------taking the square root
√y^2=√0^2
y=∓ 0

y= 0
y-0
getting the ordered pair (0,0) [Note: Zero, 0, is neither a positive nor a negative number, since it is neither greater nor less than itself].

It is a function! :)
Click to expand...
[Note: Zero, 0, is neither a positive nor a negative number, since it is neither greater nor less than itself]
So 7, for example, is neither a positive nor a negative number, since it is neither greater nor less than itself. You do realize that is pure nonsense?!

Is y^2 = x^2 a function or not? So far you said both! Well which is it?
The test for a function is if you can find an input value, usually called x, that gives back more than one output values, usually called y, then the relationship is NOT a function.

In y^2 = x^2, just because when x=0 there is just one y value does NOT mean that you have a function. Why not? Because, for example, when x=1 y can be +/- 1. Since you found an x value that has more than one y value, y^2 = x^2 is NOT a function.
 
Is y^2 = x^2 a function or not? So far you said both! Well which is it?

No, I said that regarding our problem in the Op this was not a function

Then you asked me if x were equal to 0 ( and used the same equation as in the first choice of the OP) if that was a function or not.
I performed the substitution and found y to be = 0
So I thought, erroneously I see now, that if I have x =0, y=0
Then I had an input to which corresponded only one output, the output being 0, so I thought it was a function.
But I was wrong. Thanks for the clarification.
 
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