Functions as a Family of Structures: Math Unit 1, Grade 12 (Letters & Devotion)

Description

Functions as a Family of Structures is Unit 1 of Precalculus: Functions, Trigonometry, and Mathematical Modeling (Grade 12), the Letters & Devotion Math course, complete in one printable PDF: 9 lessons, the unit check-up and the answer key, 77 pages.

• The four structural tests (constant difference, constant ratio, finite roots, domain/asymptote restriction) used to distinguish linear, exponential, polynomial, and rational families
• Family classification of tabular data using structural tests under realistic (non-clean) conditions
• The distinguishing structural assumption between two function families whose graphs look alike over a restricted domain
• Correspondence between a real-world process description and a function family’s structural assumption
• End behavior of a function family as a testable real-world prediction, checked against domain constraints
• The reverse-order undoing structure of an inverse function, expressed verbally prior to symbolic representation
• Symbolic construction and numeric verification of an inverse function for an untaught multi-step process
• Family selection and falsifiability justification for real, previously unseen data sets
• Comparative rate-of-change behavior across linear, polynomial, and exponential families

Every lesson is written for a parent with no teaching background: it opens with a short script to read aloud, names the specific wrong idea a student is likely to reach for and how to correct it, and closes with a practice sheet you may copy for your household. Scripture references are King James Version throughout. Black-and-white, 8.5 x 11 in. The whole year of this course is also in this store as a single book.

AI note: The written content of this resource was drafted with AI tools, then reviewed and edited by the author.