Absolute Value as Piecewise Function

Given an expression like $|x - a|$ , its piecewise form is:

|x - a| = \begin{cases} x - a, & \text{if } x \geq a \\ -(x - a), & \text{if } x < a \end{cases}

Rewrite $f(x) = |x - 2|$ as a piecewise function:

f(x) = \begin{cases} x - 2, & \text{if } x \geq 2 \\ - (x - 2), & \text{if } x < 2 \end{cases} = \begin{cases} x - 2, & x \geq 2 \\ - x + 2, & x < 2 \end{cases}

This representation is useful when:

Note	Folder	Status
Definition of Absolute Value		evergreen
Limit with Absolute Value - Piecewise Behavior		rough
Limit with Absolute Value - Jump Discontinuity		growing
Function Notation		evergreen
Differential Calculus		evergreen
When a Limit Exists		evergreen
Notation of a Limit		evergreen
Computing Basic Limits - Direct Substitution		evergreen
Computing Limits with Algebraic Simplification		evergreen
Limit with Difference of Cubes		evergreen

Kris's working notes