Foundations of Functions
Build a rigorous foundation in function concepts — notation, domain and range, transformations, composition, and inverses — that every later unit depends on.
Estimated Time
3–4 weeks
Difficulty
Intermediate
Overview
Unit description, learning objectives, and skills.
Unit 1 — Foundations of Functions is the launchpad for all of Precalculus. You will sharpen your use of function notation, master domain and range, and study how functions change using average rate of change. You will then combine functions through composition, transform any graph by shifting, stretching, or reflecting it, and close the unit with absolute value and inverse functions — two ideas that appear throughout calculus and every STEM field.
Learning Objectives
By the end of this unit, you will be able to:
Skills You Will Master
Real-World Connection
Functions are the language of every quantitative field. Engineers use function composition to model multi-stage processes. Economists use inverse functions to find break-even prices. Doctors use domain restrictions to ensure drug dosages stay in safe ranges. Transformations let animators and game designers move and resize objects on screen. Every concept in this unit is a tool you will reach for again and again — in calculus, statistics, physics, and beyond.
Chapter Checklist
Recommended steps for completing each chapter
- Read the Workbook
- Complete the Independent Study
- Finish the Exit Ticket
- Take the Quiz
- Review the Answer Key
- Continue to the Next Chapter