Calculus

Section 1.2 Things

Piecewise Functions

A piecewise function is a function that is made up of different functions that are "pieced" together. The pieces are called branches of the function. For example: $$f(x)=\Bigg \{ \begin{array}{lc} \sqrt{x+3}, & \text{if }x\geq -3 \\ -x^2-6x-12, & \text{if }x < -3 \end{array}$$ Here the branches are defined for different domains: when $x< -3$ the function is quadratic and when $x\geq-3$ the function is the root. Using a graphing calculator, or other graphing software, by restricting the domain we can generate only that branch and accurately show the graph:

Example For the graph below find a formula that defines this piecewise function.

Other than asking for a value, like $f(5)$, most questions involving piecewise functions will require analyzing a graph.