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Math Help - Symetry

  1. #1
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    Symetry

    Hi, i hadd a problem y= ((8)/(x^3))-((6)/(x))
    I need to know hoe the graph is symetric with respect to the
    1)x axis
    2)y axis
    3)origin
    I just needed to know the analytical way to find it without looking at the graph
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  2. #2
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    Quote Originally Posted by calc_help123 View Post
    Hi, i hadd a problem y= ((8)/(x^3))-((6)/(x))
    I need to know hoe the graph is symetric with respect to the
    1)x axis
    2)y axis
    3)origin
    I just needed to know the analytical way to find it without looking at the graph
    The graph of a function is symmetric with respect to:

    - the y-axis if f(x) = f(-x) for all x \in domain

    - the origin if f(x) = -f(-x) for all x \in domain

    If a graph is symmetric to the x-axis it is not the graph of a function:

    For every x-value you have pairs of y-values such that y_1 = -y_2

    To your function: f(x)=\dfrac8{x^3} - \dfrac6x = \dfrac{8-6x^2}{x^3}

    a) Symmetry to the y-axis:

    \dfrac{8-6x^2}{x^3} = \dfrac{8-6(-x)^2}{(-x)^3}

    \dfrac{8-6x^2}{x^3} \neq -\dfrac{8-6(x)^2}{(x)^3}

    That means: No symmetry to the y-axis.

    b) Symmetry to the origin:

    \dfrac{8-6x^2}{x^3} = -\dfrac{8-6(-x)^2}{(-x)^3}

    \dfrac{8-6x^2}{x^3} = \dfrac{8-6(x)^2}{(x)^3}

    That means: Symmetry to the origin.
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