Function of x

Y is a function of X if for every X there is only one value of Y. You should be able to look at the two equations below and see that that is true in one, not in the other. If you graph them, it might be more obvious.

1. x^2 + y^2 = 4

y^2 = -x^2 + 4

sqrt{y^2} = sqrt{-x^2 + 4}

y = -sqrt{-x^2 + 4}, y = sqrt{-x^2 + 4}

Here, y is not a function of x. Here, y represents two values.

2. x^2 − y = 12

-y = -x^2 + 12

y = (-x^2 + 12)/(-1)

y = x^2 - 12

Here, y represents a function of x.

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