I have this relation, and if graphed on Desmos.com looks very symmetrical.
$$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 1 $$
It has cusps(vertical tangents on the y-axis).
How can one determine if this relation is Even or Odd, without rearranging and solving for y.
I only recall how to find Even and Odd property of a function and not a relation.
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$\begingroup$It's even if you get the same equation when replacing $x$ with $-x$. It's odd if you get the same equation when replacing both $x$ and $y$ with $-x$ and $-y$.
Graphically, it's even if it is symmetric across the y axis via mirror reflection, and odd if it has 180 degree rotational symmetry around the origin
In this case, since both variables are squared, it is both even and odd. However, we usually don't use those terms for non-functions
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