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Math Help - Equation of a circle

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    Equation of a circle

    If S is a circle with radius 2, why is the upper half of the circle the graph to the function f(x)= (root)(4-x^2) ? What would be the function to the lower half of the circle? (I'm guessing -(root)(4-x^2), but why?)

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    Quote Originally Posted by gralla55 View Post
    If S is a circle with radius 2, why is the upper half of the circle the graph to the function f(x)= (root)(4-x^2) ? What would be the function to the lower half of the circle? (I'm guessing -(root)(4-x^2), but why?)

    Thanks!
    You're correct. The equation of a circle with radius 2 at the origin is x^2+y^2=4. If you solve this for y you get y=\pm\sqrt{4-x^2}. This isn't a function since there are going to be two values of y for every x. It doesn't pass the vertical line test. However, you can represent either the top or the bottom as a function by simply defining a function as either \sqrt{4-x^2} or -\sqrt{4-x^2}
    Last edited by adkinsjr; November 14th 2009 at 05:47 PM.
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    Thank, you very much! Makes perfect sense.
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