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Analyzing Symmetry and Conditions of Functions in Cartesian Coordinates

This document explores various functions defined in Cartesian coordinates, focusing on their symmetry and restrictions in relation to the axes and the origin. The analysis includes the conditions under which specific expressions do not sum to zero and factors influencing the relationship between x and y. Each function's behavior with respect to the x-axis, y-axis, and origin is evaluated, emphasizing cases where negative counterparts exist, impacting the overall symmetry and functional definitions.

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Analyzing Symmetry and Conditions of Functions in Cartesian Coordinates

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  1. 2- Y=X/1+X^2X_AXIS (X,Y) _(x,-y)-y dose not equal x/1+x^2 no sum about x-axisy_axis (x,y)_(-x,y)y not equal –x/1+x^2 no sum about y-axisOrigin (x,y)_(-x,-y)-y not equal –x/1+x^2 no sum about origin3- y^2=x^2+1/x^2-1x-axis (x,y) _ (x,-y)-y^2 not equal x^2+1/x^2-1 no sum about x- axisy-axis (x,y) (-x,y)y^2-=x^2+1/x^2-1origin (x,y)_(-x,-y)-y^2not equal x^2+1/x^2-1 no sum about origin4_ y=root a-x^2x-axis (x,y)_(x,-y)-y not equal root a-x^2 no sum about x- axisy-axis (x,y)_(-x,y)y not equal root a+x^2 no sum abot y-axisorigin (x,y)-(-x,-y)-y not equal root a+x^2 no sum about origin

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