What does it mean when a graph or a point on the Cartesian plane is symmetric about the origin or with respect to the origin?
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Have you searched for an answer yet? – Jared May 13 '14 at 22:23
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Take a point, rotate it around the origin by 180 degrees. It there is another point exactly there, that point is symmetric around the origin. The same exercise works for functions and relations. – Eleven-Eleven May 13 '14 at 22:24
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That $f(-x)=-f(x)$ for all $x$.
Geometrically, this means that if you reflect the graph of $f$ about one axis and then the other, the graph will land back on top of itself (i.e., you'll get the original graph again).
Same idea with a point $P(x,y)$: $Q(-x,-y)$ would be the corresponding point symmetric about the origin.
JohnD
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