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