AP Calculus AB and BC glossary
Range
The range of a function is the set of all output values it actually attains. Calculus finds it by locating the absolute extrema and checking end behavior, rather than by guessing from the formula.
On a closed interval a continuous function attains both an absolute maximum and an absolute minimum, so the range is the closed interval between them. That is exactly what the Extreme Value Theorem guarantees.
The mistake
Confusing range with domain. The domain is what you are allowed to put in; the range is what actually comes out.
Appears in: Unit 1: Limits and Continuity, Unit 5: Analytical Applications