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Thread: axis of symmetry (n > 2)

  1. #1
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    axis of symmetry (n > 2)

    There is axis of symmetry in equations that have degree greater than 2 (n > 2)?
    How can I find the axis of symmetry in these equation?
    There are equations with degree greater than 2 that have not at all axis of symmetry?
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  2. #2
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    Re: axis of symmetry (n > 2)

    How can I find the axis of symmetry in these equation?
    Symmetry tests for x-axis, y-axis and about the origin can be found here
    Algebra - Symmetry

    A graph will have symmetry about the x-axis if we get an equivalent equation when all the ys are replaced with y
    A graph will have symmetry about the y-axis if we get an equivalent equation when all the xs are replaced with x
    A graph will have symmetry about the origin if we get an equivalent equation when all the ys are replaced with y and all the xs are replaced with x.
    Quote Originally Posted by policer View Post
    There is axis of symmetry in equations that have degree greater than 2 (n > 2)?
    Degree is specific to polynomial equations, but the tests above could be for any graph.
    y = x^4 is an example of a polynomial 'even function' with axis of symmetry about the y-axis. in general, if x^n when n is even, it will be symmetric about the y-axis

    Quote Originally Posted by policer View Post
    There are equations with degree greater than 2 that have not at all axis of symmetry?
    y = x^3 is an example of a polynomial 'odd function' that has symmetry about the origin, but doesn't have an "axis of symmetry." In general, if x^n when n is odd, it will be symmetric about the origin.
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    Re: axis of symmetry (n > 2)

    Quote Originally Posted by MacstersUndead View Post
    Symmetry tests for x-axis, y-axis and about the origin can be found
    y = x^3 is an example of a polynomial 'odd function' that has symmetry about the origin, but doesn't have an "axis of symmetry." In general, if x^n when n is odd, it will be symmetric about the origin.
    Can you an example to n = 6?

    What is the equation?

    And: Can you an example to equation with non-symmetry axis when n = 6?
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    Re: axis of symmetry (n > 2)

    Quote Originally Posted by policer View Post
    Can you an example to n = 6?

    What is the equation?
    Do you mean when y = x^6 ?
    6 is even, so it will be symmetric about the y-axis. Check using the second test that the graph has symmetry about the y-axis.

    And: Can you an example to equation with non-symmetry axis when n = 6?
    y = x^6 + x^3 is one example, an "even" function plus an "odd" polynomial function (x^6, x^3, respectively.)
    https://en.wikipedia.org/wiki/Even_and_odd_functions
    The sum of an even and odd function is neither even nor odd, unless one of the functions is equal to zero over the given domain.
    The page also includes other ways to determine if functions are "even" or "odd", including basic calculus properties.
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  5. #5
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    Re: axis of symmetry (n > 2)

    What do you mean by "non-symmetry axis"? Any line that is not an axis of symmetry?
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