SOLUTION: how to determine whether the equation defines y as a function of x. is it a function yes or no to the problem: x=y^2-6 and problem y=x^2+6

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Question 585845: how to determine whether the equation defines y as a function of x. is it a function yes or no to the problem: x=y^2-6 and problem y=x^2+6
Found 2 solutions by KMST, chimm:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
+y=x%5E2%2B6 defines y as a function of x, because for every x value there is no more than a y value. (In fact for every x there is exactly one y value). We can forgive a function if some values of x do not have a y, but if there is more than one y for even one value of x, then the relation is not a function.
x=y%5E2-6 does not define y as a function of x, because some value(s) of x have more than one y.
In general,
x=y%5E2-6 --> x%2B6=y%5E2 --> y=sqrt%28x%2B6%29 or y=-sqrt%28x%2B6%29
So, all the values of x larger than -6 would have two y values.
For example, x=10 would be paired with y=4 and y=-4.
A function cannot assign more than one y to any x value.

Answer by chimm(1) About Me  (Show Source):