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About This Course

Welcome from Rick

Hi there! I'm Rick the Raccoon, and I'll be your guide through every twist, turn, and asymptote in this course. Don't let the mask fool you — I'm not here to steal your lunch, just to help you master functions. I love a good math pun, I celebrate every small win, and I genuinely believe that every input has its output. Whenever a concept starts to feel intimidating, look for one of my admonition boxes — I'll pop in with a tip, a joke, a gentle warning about common mistakes, or a bit of encouragement to keep you moving. We're going to explore domains and ranges, graph every shape imaginable, and transform parabolas into things of beauty. So grab a pencil, loosen up your graphing calculator, and let's map this out together!

Why Functions Matter

The concept of a function is the central, unifying theme of modern mathematics. Nearly every topic a student will encounter after algebra — calculus, statistics, physics, economics, machine learning — is built on the idea of one quantity depending on another. Here are some statistics that demonstrate the reach of this subject:

Globally (2026 projections):

  • Over 170,000 students sit the International Baccalaureate Diploma Programme mathematics exams each year across more than 150 countries
  • Approximately 3.8 million students take a first high school course built around functions (Algebra 2, Pre-Calculus, or equivalent) each year in the United States alone
  • Functions are a prerequisite for the roughly 800,000 high school students and 700,000 college students who study calculus each year

These numbers represent millions of students working to master the same concepts you'll learn in this course. You're joining a global community of learners building the mathematical foundation for everything that comes next — calculus, data science, engineering, and beyond.

Rick Can Help You Save Some Coins

Rick sharing a tip Did you know that traditional IB and pre-calculus textbooks often cost between $80 and $150? That's a lot of allowance money before you even start learning! And here's the real kicker — those textbooks can't let you drag a slider and watch a parabola transform in real time.

I believe every student deserves access to high-quality mathematics education, regardless of their budget. That's why this entire textbook is free and open source, with 28 interactive MicroSims that let you explore function concepts hands-on. No paywalls, no access codes, no "edition 12 with slightly rearranged exercises."

Every input has its output — and your output here is a solid understanding of functions without breaking the bank. Let's map this out together!

Learning Through Interactive Visualization

This course takes a fundamentally different approach to teaching functions. Instead of drowning in abstract notation, you will build deep intuition through 28 interactive MicroSimulations. These browser-based visualizations let you experiment with gradients, intercepts, transformations, asymptotes, and function composition in real-time.

Watch a function and its inverse reflect across the line \(y = x\). Drag roots to see how polynomials bend and cross. Feed inputs through two function machines and watch how composition order changes the result. Adjust a base and see exponential growth morph into decay at \(a = 1\). These are not passive animations — they are hands-on laboratories where you control the parameters and discover the concepts yourself.

You Will Have Fun

Yes, you read that right. This course is designed to be genuinely enjoyable. The MicroSims turn abstract concepts into interactive playgrounds. The connections to real-world applications — projectile motion, compound interest, population growth, half-life decay — give every topic immediate relevance. And Rick the Raccoon will be there with a joke, a pun, and a well-timed nudge whenever a concept starts to feel intimidating.

Whether you are preparing for IB exams, building the foundation for calculus, or simply want to understand the mathematical structures that describe the world around you — this course will give you the tools, the intuition, and the confidence to succeed.

Let's explore the beauty of functions together!

Background

The concepts covered by this book were generated by the following prompt:

Prompt

What are the core topics and learning objectives for the International Baccalaureate Diploma Programme Mathematics "Functions" syllabus, covering both Standard Level (SL) and Higher Level / Additional Higher Level (HL/AHL)?

Our tools have also matured since January 2025 when we first started using AI to generate textbooks. This version of our intelligent textbook was generated using Claude Code Skills, with a strong focus on creating high-quality MicroSims that bring abstract function concepts to life.

About the Author

Dan McCreary is a semi-retired AI researcher with too much time on his hands. After three decades helping Fortune 100 organizations reason over massive datasets — including founding the Generative AI Center of Excellence at Optum and building one of the world's largest healthcare knowledge graphs (over 25 billion vertices) — he now channels his considerable free time into generating interactive intelligent textbooks at a rate that alarms his family and mystifies his neighbors.

He is the co-author of Making Sense of NoSQL (Manning Publications), the founding chair of the NoSQL Now! conference, and a person who has produced over 70 intelligent textbooks in roughly the time it takes most authors to outline one. You can visit the Intelligent Textbooks Case Studies to see the evidence. He has been a STEM volunteer since 2014, which provides a thin veneer of respectability to what is otherwise a compulsive hobby of using AI to generate interactive intelligent textbooks.

Selected Credentials

  • B.A. in Physics and Computer Science from Carleton College
  • M.S.E.E. from the University of Minnesota
  • MBA coursework at the University of St. Thomas
  • Patent holder in semantic search and ontology management techniques
  • Advocate for large-scale Enterprise Knowledge Graph adoption across healthcare and education
  • Long-time promoter of accessible, low-cost AI-powered learning experiences
  • Creator of over 70 interactive intelligent textbooks, a number that continues to grow at a rate that concerns his family

Note

IB® and International Baccalaureate® are registered trademarks of the International Baccalaureate Organization, which is not affiliated with, and does not endorse, this product.