Piecewise Functions Worksheet

Sample problems

For each problem, decide which piece applies to the given input (mind whether the endpoint uses $<$, $\le$, $>$, or $\ge$), then evaluate. Use exact values.

1. 1. Let $f(x)=\{\begin{array}{ll}2x+1& x<0\\ x^2& x\ge 0\end{array}$ Find $f(-3)$.
2. 2. Using $f(x)=\{\begin{array}{ll}2x+1& x<0\\ x^2& x\ge 0\end{array}$, find $f(4)$.
3. 3. Using $f(x)=\{\begin{array}{ll}2x+1& x<0\\ x^2& x\ge 0\end{array}$, find $f(0)$. (Be careful which piece includes $x=0$.)
4. 4. Let $g(x)=\{\begin{array}{ll}-x& x\le -1\\ 3& -1<x<2\\ x-1& x\ge 2\end{array}$ Find $g(-4)$.

Plus 9 more problems and a full answer key in the PDF.