# Absolute Value Function Definition

In mathematics absolute value is defined as the value which is equals to both positive value and negative value. Let us say if absolute value of 4 is 4 then absolute value of -4 is also 4. We call absolute value as modulus. This absolute number is a real number. Absolute value can be used to calculate the distance of an object.

A real value absolute function is a continuous function for every Point. We can say that Absolute Value Function is differentiable at each and every point except point at x = 0. This absolute function is not defined at point x = 0. Absolute value functions have this property that they are idempotent in nature, which means that if we apply value many times we get same value that we get first time.

An absolute function is a function which continuously decreases in interval -∞ to 0, we represent it as interval (-∞, 0] and absolute function continuously increases in interval 0 to positive infinity, we represent it as interval [0,+∞). As we know from definition of absolute number that absolute value for both positive and the negative value are same, so we can say that absolute value function has real number value and it is invertible in nature.

These absolute value Functions are of two types: Real and Complex.

Absolute Value of a Real Number:
The absolute value of a real number is the number's distance from the origin to the real number in the real number line. Also the absolute value of the difference of two Real Numbers is the distance between those two real numbers on the real number line.
e.g, |x| = |-x| = x

Absolute Value of a Complex Number:
The absolute value of a complex number is the number's distance from the origin to the complex number in the complex plane. Also the absolute value of the difference of two complex numbers is equal to the distance between those two complex numbers on the Complex Plane.
e.g, |x+iy| = $\sqrt{x^{2}+y^{2}}$