Determine whether the graph of the relation is symmetric with respect to the y axis, x axis, or the origin.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: Symmetry about the origin?

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