Which of the following rules represents a function?

y=x^2 is the equation that shows/ represent a function.
but what about if i have to do it without the graphing software. it will take some precious time to do it by hand at a timed test.
there is no other way to determine that without graphing it.
maybe because the shape in which the equation is rider, right?. drop a hint there, thanks, BBB
 
eddy2017 said:
y=x^2 is the equation that shows/ represent a function.
but what about if i have to do it without the graphing software. it will take some precious time to do it by hand at a timed test.
there is no other way to determine that without graphing it.
maybe because the shape in which the equation is rider, right?. drop a hint there, thanks, BBB
Click to expand...
Pick a positive and a negative value of x. Let's say -1 and 1. Plugin the equations. If you get the same y value for two different x then it's not a function. It's the same as failing the vertical test.
 
BigBeachBananas said:
Pick a positive and a negative value of x. Let's say -1 and 1. Plugin the equations. If you get the same y value for two different x then it's not a function. It's the same as failing the vertical test.
Click to expand...
thank you, that's clever. I'll post it and see.
 
let's ee what y values i get when i plug the x values
y^2=x^2
y^2=1^2
y^2=1

y^2=-1^2
y^2=1

I like the table because it helps me see it better
x y
1 1
-1 1
Got the same values for y so it is not a function. got it, buddy. than you. if you want me to post the rest you tell me. but I see it. thanks
 
but I' m in doubt now because when i plug the 1, -2 values in
y=x^2 (which we determined to be the choice when we graph it) I am also getting the same y value????

y=1^2
y=1

y=-1^2
y=1
?????
 
eddy2017 said:
but I' m in doubt now because when i plug the 1, -2 values in
y=x^2 (which we determined to be the choice when we graph it) I am also getting the same y value????

y=1^2
y=1

y=-1^2
y=1
?????
Click to expand...
My mistake, I might have told you wrong. Try this again. Pick a value of x, if you can get 2 values of y for the same x then it's not a function.
so for equation 1 x^2=y^2.
For x=1, you can get y=-1 or 1. so it's not a function.
Try again for others.
 
X=2
y=x^2
y=4
----------------
x=-2
y=-2^4
BigBeachBananas said:
My mistake, I might have told you wrong. Try this again. Pick a value of x, if you can get 2 values of y for the same x then it's not a function.
so for equation 1 x^2=y^2.
For x=1, you can get y=-1 or 1. so it's not a function.
Try again for others.
Click to expand...
let me see if i understand
if i give x the value of 1 I can get values for y of -1 and 1. that is what you're saying here.
let's see
x^2=y^2
1^2=y^2
1=y^2

how can get y=-1 ????. I don't understand your explanation. it should be easy, but i am getting confused

Pick a value of x, if you can get 2 values of y for the same x then it's not a function.
so for equation 1 x^2=y^2.

above I pick one value for x and I only get one value for y. So?. You are not getting thru to me, BBB.
 
eddy2017 said:
1=y^2
Click to expand...
When you take the square root, you actually get two values
[math]\sqrt{1}=\sqrt{y^2}[/math][math]1=|y|[/math][math]\pm 1=y[/math]
To see this is true:
For y=-1 =>(-1)^2=1.
For y=1=>(1)^2=1
In conclusion, for x=1, you get y=-1 or y=1. So it's not a function.
 
I see. the equation that represents a function gives only one value for y. that is why it is a function. Because there is one y value for the x value inputted , and only one.
y=x^2
y=4

I see it clearly now. thank you.
 
A) y^2 = x^2
If x=2 for example, how many different values for y?

B) y=x^2.
If you square any value, how many values do you get? y equals does value(s).

C) |y|= x^2.
You you square some number, how many different values might y be?

D) y^2 = x
If you randomly pick some value for x, then how many different values might there be for y?

Answering the questions above should inform you whether or not each given relation is a function or not.
 
A) I'll take the square root of x so y will have to values. Positive and negative
B) if you square the x you only get one value.
eg x^2 =4
C)= only one value. Absolutely bars mean that the absolute value of y is y.
D) y is squared so I'll get only one value.. the value of the number squared to whatever number is squared to.
 
Last edited:
eddy2017 said:
A) Two values +2, -2
B) if you square the x you only get one value.
eg x^2 =4
C)= only one value. Absolutely bars mean that the absolute value of y is y.
D) y is squared so I'll get only one value.. the value of the number squared to whatever number is squared to.
Click to expand...
B) Yes, if you square x, then you only get back one value. The question is how many y-values do you get back?

C) No! |y| = y is not always true! |-7| does not equal -7. Try again.

D) What you said is true but I have no idea why you would say it. Given an x-value how many different y-values might you get?

You are playing the game completely wrong! I give you an x-value and you need to decide if you could ever get back more than one y-value.

So saying that if you square x, you'll get back one value is meaningless in determining if the relationship is a function or not.

As I always say, you can't play the game unless you know the rules!
 
B) only one y value.
C) absolute value of -7 is 7. I can think squaring y too and so getting two values + -
 
D) y^2 = x
If you randomly pick some value for x, then how many different values might there be for y?
I will get two values for y let's say I pick 3 for x
I will get square root of 3 and - square root of 3
 
So which ones are functions! That is the question you were asked to solve.
 
The only one which is a function is B.
There is one x value and one corresponding y value.
 
eddy2017 said:
The only one which is a function is B.
There is one x value and one corresponding y value.
Click to expand...
OK, I go along with your comment that there is one x-value. Can you please tell me that one x-value?
 
eddy2017 said:
X=2
y=x^2
y=4
----------------
x=-2
y=-2^4

let me see if i understand
if i give x the value of 1 I can get values for y of -1 and 1. that is what you're saying here.
let's see
x^2=y^2
1^2=y^2
1=y^2

how can get y=-1 ????. I don't understand your explanation. it should be easy, but i am getting confused

Pick a value of x, if you can get 2 values of y for the same x then it's not a function.
so for equation 1 x^2=y^2.

above I pick one value for x and I only get one value for y. So?. You are not getting thru to me, BBB.
Click to expand...
Did you even try to see if y=-1 works? I guess not. You choose to say that you don't understand vs trying to see why y=-1 works. Not a good habit.
If x=1, then x^2 = 1.
So we get y^2=1. Someone told me that y=-1 is a solution but I don't believe them! But I'll check anyways! (-1)^2 = 1. Wow, that is actually true.
 
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.

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

-----------------------------------------------
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
-------------------------------------------


|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
 
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