Piecewise, Step, and Absolute Value Functions
I can evaluate piecewise, step, and absolute value functions using the correct rule.
The problem this sheet solves
With piecewise, step and absolute value functions the mechanics are manageable and the boundary is not. At a break point a student has to know that OPEN excludes and CLOSED includes, and without that they choose by position on the page. Choosing the correct piece for a given x is the other half, and it is the step most often skipped entirely. This sheet makes finding the right piece the first move, then makes the open and closed convention explicit and tests it at the boundary where it decides the answer. Piecewise, step and absolute value are treated as one family rather than three topics, which is what stops students learning three unconnected procedures.
The key rule
Find which piece's domain contains your x-value, then use ONLY that piece's rule — at a boundary, the closed point is the real answer, never the open one.
Closed counts. Open doesn't.
Watch out
The mistake: A student sees an open circle at (4, 2) and a closed circle at (4, 3), and answers f(4) = 2 because it's drawn first, on the left.
The fix: Position means nothing — OPEN excludes, CLOSED includes. f(4) = 3, the closed point's value, regardless of appearance.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.