What is the symmetry to y-x3?

Answer 1

Let F(x,y) = y - x^3

Note that (-x)^3 = -(x^3)

This suggests that

F(-x,-y) = -F(x,y)

(-x,-y) represents the point (x,y) reflected through the origin. You could say the function F has anti-point symmetry -- each point (x,y,F) is reflected through the origin at (-x, -y, -F).