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Symmetry about the origin?

  1. Mar 17, 2008 #1
    Determine whether the graph of the relation is symmetric with respect to the y axis, x axis, or the origin.

    y=[tex](x-3)^{3}[/tex]

    I don't know how to produce a visual of the graph with this post but it is a graph of y=[tex]x^{3}[/tex] moved 3 units to the right along the x axis. Visual examination of the graph tells me that the equation is not symmetrical about the y axis, the x axis or the origin.
    Using the tests for symmetry seem to confirm this.
    For y symmetry: substituting -x for x does not yield an equivalent expression.
    For x symmetry: substituting -y for y does not yield an equivalent expression.
    For symmetry about the origin: substituting -x for x and -y for y also does not yield an equivalent expression. I get y=[tex](x+3)^{3}[/tex]
    The answer given on the answer sheet is that the expression is symmetric about the the origin. I am not seeing this.

    Thanks for any replies.
     
  2. jcsd
  3. Mar 18, 2008 #2

    HallsofIvy

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    Staff Emeritus
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    y= (x- 3)2 is clearly not symmetric about the orgin. It is symmetric about the point (3, 0). Perhaps that was what was meant- or it is just a typo.
     
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