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Math Help - Determining whether an equation represents a function.

  1. #1
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    Determining whether an equation represents a function.

    I have two questions of the sort. The first one is x^2 + y^2 = 4 and I reorganized to look like y =(-x^2 +)^1/2. At first, I sensed it to be a function, but I was found to be wrong. Can someone explain why it is not a function, the same goes for the second equation y^2 = x^2 - 1, which I change into y = (x^2 - 1)^1/2. Thank you.
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  2. #2
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    Re: Determining whether an equation represents a function.

    When you take the square root, you must take both the positive and negative square roots. The equation

    x^{2}=1

    has two real solutions. Thus, because what you actually have for the first equation is

    y=\pm\sqrt{4-x^{2}},

    you can see by inspection that it's not a function, since one x value in the domain maps to two different y values.
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