If a function has a symmetry, it is either even or odd. The symmetry is odd when the graph is symmetric about the origin.

If a function has odd symmetry, the rule it must follow is $$f(\text{-}x)=\text{-}f(x).$$ An odd symmetry means graphically that the graph is rotated $180^{\circ }$ about the origin. Therefore, changing the sign of the $x$-value also changes the sign of the function value.

If this rule is satisfied on the entire domain, the function has odd symmetry.