Absolute Value - Absolute Value Function

Absolute Value Function

The real absolute value function is continuous everywhere. It is differentiable everywhere except for x = 0. It is monotonically decreasing on the interval (−∞,0] and monotonically increasing on the interval [0,+∞). Since a real number and its negative have the same absolute value, it is an even function, and is hence not invertible.

Both the real and complex functions are idempotent.

It is a piecewise linear, convex function.