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Absolute Value Function 📂Functions

Absolute Value Function

Definition

A function defined as ff is called the absolute value function, and its values are denoted as shown in ∣x∣|x|.

∣x∣:=f(x)={xif x>00if x=0−xif x<0,x∈R |x| := f(x) = \begin{cases} x &\text{if } x>0 \\ 0 &\text{if } x=0 \\ -x &\text{if } x<0 \end{cases},\quad x\in \mathbb{R}

Explanation

Absolute value refers to the magnitude of a real number, and a generalization of this is the norm. The triangle inequality holds.

∣x+y∣≤∣x∣+∣y∣,x∈R |x + y| \le |x| + |y|,\quad x \in \mathbb{R}