# Absolute Value Function

In mathematics, the absolute value of any real number is the non-negative value of that number without regard to its sign. It is similar to the distance of any number from zero in a number line. For example, if we have to find the value of |12| and |-12|, then it is 12. Because absolute value of -12 is 12, and the absolute value of 12 is also 12. This function is one of the most used functions in mathematics. Absolute value is used in various fields of mathematics like in complex numbers, ordered rings, quaternions and vector spaces.

Absolute value function (also known as mod function) is defined as:

f(x) = |x| = $\left\{\begin{matrix}

x &;x \geq 0 \\

-x&; x <0

\end{matrix}\right.$

x &;x \geq 0 \\

-x&; x <0

\end{matrix}\right.$

This function is closely related to the notation of distance, norm and magnitude in various physics and mathematical contexts.

Notaion of absolute value function : f(x) = |x|

It is also sometimes written as : abs (x)

The graph of |X| makes a right angle at origin.

**Graphically this can be shown as follows:**

The domain of Absolute value function is R (real numbers)

The range of the same is All Positive Real Numbers [0,+$\infty$).

**The absolute value parent function is:**

**y = |x|**