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Even, Odd, or Neither?

  1. Feb 24, 2004 #1
    Is the function x^3 - x + 1 even, odd, or neither? When I graphed this, it looked like it was symmetric about the origin, so I thought that it might be an odd function. Either that or it is neither?
  2. jcsd
  3. Feb 24, 2004 #2
    A function is even if:

    f(-x) = f(x)

    A function is odd if:

    f(-x) = -f(x)

    So to figure out if it's even of odd, plug in -x in place of x and compare it to the original.

  4. Feb 24, 2004 #3
    Look at graph

    Also I believe that odd fuctions are rotationaly symetric while even fuctions are symetic on the vertical line. (When a graph is fliped horizontally over it)
  5. Feb 24, 2004 #4

    matt grime

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    f(0) isn' 0 so it certainly isn't odd, and clearly it isn't even.

    hint: a polynomial in x is even (odd) iff the powers of x are all even (odd)
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