SOLUTION: Which of these equations represent FUNCTIONs check all that apply 3x^2 - 2y^2=1 Y=x^2 Y=4X Y^2=X^2

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Question 930632: Which of these equations represent FUNCTIONs check all that apply
3x^2 - 2y^2=1
Y=x^2
Y=4X
Y^2=X^2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A function, often written as y=f%28x%29 , defines y (dependent variable) as a function of x (independent variable).
That means that every time you feed a certain value for x to the function machine,
that machine always does the same thing, reliably.
It either always spits the same value for y,
or it cannot calculate any y value.

y=x%5E2 defines y as a function of x ,
because for each x it no more than one y ,
so given an x , we have no doubts about what y (if any) that x is paired with.
y=4x defines y as a function of x ,
because for each x there is no more than one y ,
so given an x , we have no doubts about what y (if any) that x is paired with.
y=4x<--->x=y%2F4 also defines x as a function of y ,
because for each y there is no more than one x ,
so given a y , we have no doubts about what x it is paired with.

3x%5E2-2y%5E2=1 and y%5E2=x%5E2 do not define any function,
because they pair the same x with two different values of y,
and the same y with two values of x .