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}

:PROPERTIES: :CUSTOM_ID: example :END: 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: - Solving equations involving $|x - a|$ - Graphing the function - Performing algebraic analysis

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