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Is a circle a function?

  1. Jan 13, 2005 #1
    I was brought up believing that when a mapping had more than one ordinate (y) for a particular abscissa (x), it did not describe a function. So is a circle not a function?
     
  2. jcsd
  3. Jan 13, 2005 #2
    correct..................
     
  4. Jan 13, 2005 #3

    dextercioby

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    The so-called "vertical test" will always tell u the answer.In the case of the circle,there are an infinite number of portions/arches (is this the word?? :confused: ) which are functions.

    Daniel.
     
  5. Jan 13, 2005 #4

    matt grime

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    <pointing out what a function is> A function from where to where?
     
  6. Jan 13, 2005 #5

    Galileo

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    There is some semantics involved.
    Since a circle is a geometrical figure, the wording: 'is a circle a function' has no meaning.
    For the same reason, a parabola is not a function, but the graph of the function is.

    ...doh, I `m getting old and picky. Nevermind... :redface:
     
  7. Jan 13, 2005 #6

    HallsofIvy

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    Indeed, even if we interpret "is a parabola a function" to mean "is a relation whose graph is a parabola a function" we would have to specify the coordinate system. A parabola whose axis is parallel to the y-axis corresponds to a function but exactly the same parabola, in a rotated coordinate system would not be.

    (Notice I switched from "circle" to "parabola". A circle, in any coordinate system, does not correspond to a function.)
     
  8. Jan 13, 2005 #7
    In any carthesian coordinate system.
    In a polar coordinate system, it does.
     
  9. Jan 13, 2005 #8

    NateTG

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    I mathematics, a function is a sort of black box - you put something in, and it spits something out. (There are other ways to think of them as well.) Now, you ask whether a circle is a function, and the answer is clearly no, since a circle is typically a set of points.

    In the familiar (I suppose it could be called cartesian) system, there is no function that whose plot is a circle. In a polar or parametric system functions can readily have circular plots.

    It is also relatively easy to see that:
    [tex]f(x)=\sqrt{1-x}[/tex]
    generates the plot of a half circle - which can often be used instead.
     
  10. Jan 14, 2005 #9
    That is: [tex]f(x)=\sqrt{1-x^2}[/tex]
     
  11. Jan 14, 2005 #10

    Galileo

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    The plot of
    [tex]f:[0,2\pi) \to \mathbb{R}^2[/tex]
    [tex]f(x)=(cos(x),sin(x))[/tex]

    is a circle.
    Or is this cheating?
     
  12. Jan 14, 2005 #11

    matt grime

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    This is the "non-cartesian function" people were mentioning. The question, from what i can tell, boils down to the fact that the OP thinks a graph and a function are the same thing.
     
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