Absolute value. Useful properties and graph

The absolute value [tex]|a|[/tex] of number [tex]a[/tex] may be thought of as its distance from zero. Definition of absolute value: [tex]\sqrt{a^2}=|a|=\begin{cases} a, \ \ \ \text{jei} \ \ \ a \ge 0  \\ -a, \ \ \ \text{jei} \ \ \ a<0 \end{cases}[/tex]

Useful properties: [tex]|a|\ge 0[/tex], [tex]|-a|=a[/tex], [tex]|a-b|=|b-a|[/tex], [tex]|a|-|b|\le |a+b|\le |a|+|b|[/tex]

The graph of the absolute value y=|x|