Study Guide
Learning Objectives
- Construct linear, quadratic, cubic, quartic, degree-$n$, or piecewise models from restrictions (1.14.A.1).
- Construct models using transformations of a parent (1.14.A.2).
- Construct models using technology regressions (linear–quartic) (1.14.A.3).
- Construct piecewise models by combining techniques (1.14.A.4).
- Construct rational models for inverse-proportion contexts (1.14.B.1).
- Apply a model to answer questions about data or context (1.14.C.1).
Suggested Practice Sequence
1. Two-point linear builds; slope–intercept from context. 2. Quadratic from vertex+point or zeros+$y$-intercept. 3. Transform a parent into a contextual graph. 4. Piecewise fee/rate stories; evaluate on the correct piece. 5. Rational $k/x$ or $k/d^2$ calibration. 6. Regression-language items (what the calculator gives; how to use it). 7. Apply: predict, interpret, respect domain.
Classroom / Check-In Moves
- Require “givens → equation → check a known point.”
- Color-code piecewise domains before evaluating.
- Cold-call: “What does $k$ mean in this model?”
Misconception Watch-List
- Writing type only (1.13) and stopping.
- Using the wrong piece at a boundary.
- Extrapolating wildly beyond data after a regression.
- Forcing a polynomial when inverse proportion is the story.
Vocabulary to Own
- construct; apply; restriction
- parent transformation; regression
- piecewise-defined model
- inversely proportional; rational model
- calibration constant $k$
Materials Map
- Practice: build + light apply
- Word: contextual construction
- Mixed / multi-*: link 1.13 selection → 1.14 build → apply
- Review & practice test: timed builds
- Interactive: quick checks