How to determine if the function has x-axis sym, y-axis sym, and origin sym y^2 -xy =2

To check for symmetry on the x axis, replace y with –y

-y^2 –x(-y) =2

 Apply the product rule, since the equation is not identical tot eh original equation it is not symmetric about the x axis

 Now do the same for y axis by replacing x with –x

 Again using product rule the equations are not identical, so it is not symmetric about the y axis

 To check the origin,

 Replace both x & y with –x  & -y

Again using product rule, the equations are not identical so it is not symmetric about the origin

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