Algebra 2 · Unit 1 · Topic 1.5
Piecewise Functions and Absolute-Value Models
A piecewise function applies different rules on specified parts of its domain.
Definition and explanation
A piecewise function applies different rules on specified parts of its domain. The interval conditions determine which formula is used, including what happens exactly at a boundary.
Worked example
Suppose a delivery costs C(w) = 6 dollars for 0 < w ≤ 2 kg and C(w) = 6 + 2(w − 2) for w > 2 kg. At 2 kg the cost is $6; at 3.5 kg it is 6 + 3 = $9. Each weight uses exactly one rule.
Common mistake
Applying both formulas at an endpoint can create conflicting outputs unless the interval definitions agree.
Key takeaway
A piecewise function applies different rules on specified parts of its domain.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.