Study Guide
Learning Objectives
- Identify an appropriate function type for a scenario or data pattern (1.13.A).
- Match clues: constant ROC → linear; linear ROC / unique extremum / area → quadratic; volume → cubic; multiple extrema/zeros → polynomial; constant $n$th differences → degree $n$; $n+1$ points → degree ≤ $n$; regime change → piecewise.
- Describe assumptions about consistency and covariation (1.13.B.1–B.2).
- State domain and range restrictions from math, context, or data extremes (1.13.B.3–B.4).
Suggested Practice Sequence
1. Sort stories into linear / quadratic / cubic / piecewise. 2. Read finite-difference clues from short tables. 3. Choose degree from number of points ($n+1$ ⇒ degree ≤ $n$). 4. Write assumption sentences (consistency + covariation). 5. Add domain/range restrictions for each chosen model. 6. Mixed FRQ: select type + articulate limits (no full construction yet).
Classroom / Check-In Moves
- Card sort: clue → function type.
- Require one assumption and one restriction before any equation writing.
- Cold-call: “Why not linear?”
Misconception Watch-List
- More points always means higher degree with no bound.
- Piecewise means “two formulas overlapping on the same $x$.”
- Assumptions are optional fluff.
- Domain restrictions only come from algebra (context matters too).
Vocabulary to Own
- function model; function type
- rate of change; finite differences
- piecewise-defined function
- assumption; restriction; domain; range
- consistency; covariation
Materials Map
- Practice: select type from clues
- Word: story → type + assumptions
- Mixed / multi-*: contrast nearby Unit 1 features without full 1.14 builds
- Review & practice test: timed selection fluency
- Interactive: quick checks