A function is said to be an even function if the sign of the image does not change when the sign of the preimage changes.

Conversely, a function is called an odd function when the sign of the image changes when the sign of the preimage changes.

For Even functions, f(x) = f(-x).

For the Odd function, f(x) = -f(-x).

Examples of Even Function: f(x) = x2 . We have f(1) = 1 and f(-1) = 1 hence f(1) = f(-1). This is true fora ∀ x ∈ R. Another example would be mod function |x|.

Examples of Odd Function: f(x) = x3 . We have f(1) = 1 and f(-1) = -1 hence f(1) = -f(-1). This is true for ∀ x ∈ R.