Unit 01 · 2 Weeks · 6 Lessons
Advanced Functions, Transformations & Inverses
How do notation, transformations, composition, and inverse thinking reveal the structure and behavior of functions?
Complete instructional sequence
Detailed Lessons
Lessons include objectives, formulas, concept development, worked examples, guided and independent practice, differentiated pathways, application, misconception analysis, mastery evidence, reflection, and local completion.
Function Language, Notation & Evaluation
Function notation separates the name of a relationship from the value produced at a chosen input. Evaluation means substituting an allowed input everywhere the variable appears, preserving grouping and units.
Open detailed lesson
Lesson 02Domain, Range, Intervals & Constraints
Domain restrictions come from the rule and the context. Denominators cannot be zero, even roots require nonnegative radicands in the real numbers, and real situations may restrict time, count, or measurement.
Open detailed lesson
Lesson 03Transformations of Parent Functions
Transformations describe how a parent function is stretched, reflected, and shifted. Horizontal changes act inside the input and therefore work inversely; vertical changes act directly on outputs.
Open detailed lesson
Lesson 04Function Composition & Decomposition
Composition uses the output of one function as the input of another. The order matters, and the domain must satisfy both the inner function and the outer function after substitution.
Open detailed lesson
Lesson 05Inverse Functions & One-to-One Relationships
An inverse reverses a one-to-one function. Swap input and output, solve for the new output, and verify by composition. A restricted domain may be needed before an inverse is a function.
Open detailed lesson
Lesson 06Piecewise, Absolute-Value & Step Functions
Piecewise functions use different rules on different parts of the domain. Endpoint symbols and context determine whether a boundary value is included, excluded, or shared.
Open detailed lesson
Practice and evidence
Unit Resources
Foundation Practice
Prerequisite support, smaller steps, representation aids, and correction prompts.
Core Practice
Complete standards-level definitive-answer practice and explanation.
Extended Practice
Generalization, proof, parameter analysis, technology, and deeper modelling.
Unit Mastery Check
Fresh randomized questions with scoring and explanations.
Function Transformation & Inverse Design Portfolio
Applied investigation with evidence, validation, limitations, and defense.
Family Guide
Plain-language overview, support questions, and evidence expectations.
Teacher Guide
Pacing, differentiation, assessment, misconceptions, and records.
Vocabulary Data
Core English terms with Spanish, French, Arabic, and Portuguese support.
Standards Map
Unit concepts and broad national/international alignment categories.