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(-x)=-f(x). An odd symmetry means graphically that the graph is rotated 180∘ 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.