Piecewise Functions

A piecewise function is defined by using different formulas on different parts of its domain. $$f(x) = \begin{cases} \text{formula 1} & \text{interval 1}\\ \text{formula 2} & \text{interval 2} \\ \vdots & \vdots \\ \text{formula $n$}&\text{interval $n$} \end{cases}$$

Evaluating Piecewise Functions

To evaluate a piecewise function at $x=a$, first look on the right hand side to determine which interval contains $x=a$. Then substitute $x=a$ into the corresponding formula.