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akshaybBest ResponseYou've already chosen the best response.0
Please tell the answer.
 one year ago

hewsmikeBest ResponseYou've already chosen the best response.1
May I assume that you mean test some function for symmetry across the x and y axes and the origin ? :) Generally it means applying some transformation and seeing if there is no change ie. swap x for x and see if f(x) = f(x) so with \[f(x) = x^{2}\]then \[f(x)=(x)^{2} = (1)^{2}x^{2}= x^{2}=f(x)\]if we are plotting this function in two dimensions as \[y =x^{2}\] dw:1359934489024:dwthen this implies symmetry of reflection across the yaxis ( pardon my drawing skills ). Symmetry across the xaxis is likewise. As regards the origin : then that is a reflection across the yaxis and then another reflection across the xaxis. Thus a circle dw:1359935010242:dwis symmetric across x and y axes and hence the origin too. You can deduce this from the equation for a circle, say : \[x^{2}+ y^{2} = 1\]is invariant if we swap x for x and y for y \[(x)^{2} + (y)^{2} = (1)^{2}x^{2} + (1)^2y^{2} = x^{2} + y^{2}\]To be complete I ought mention that reflections across the x then y axes ( or vice versa ) is equivalent to a rotation of 180 degrees around the origin ....
 one year ago

hewsmikeBest ResponseYou've already chosen the best response.1
Err, the circle was in that second graphic earlier today.
 one year ago
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