Absolute value function

This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
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Definition

The absolute value function, denoted as $\operatorname {abs}$ or $|\cdot |$, is defined as the function that sends a real number to itself if it is nonnegative and to its negative if it is negative.

The absolute value of $x$ is denoted $\operatorname {abs} (x)$ or $|x|$. It is defined as:

$|x|:=\left\lbrace {\begin{array}{rl}x,&x\geq 0\\-x,&x<0\\\end{array}}\right.$

Graph