Course Connections Web

Algebra 2 · Axiom Academy

SUMMARY Course Connections Web Ten content units, one web — see how functions, systems, shapes, patterns, and chance all connect into a single mathematical foundation. A function f pairs every input with exactly one output — nearly everything in this course is some family of functions being built, transformed, combined, or inverted. Inverse operations travel in pairs: exponentials logarithms, powers roots, and every transformation has an undo, f^ -1 (f(x))=x . Complex numbers complete the picture: a degree- n polynomial always has exactly n zeros once you allow — real polynomials just hide their complex zeros in conjugate pairs. Not everything is a smooth curve — Sequences & Series and Probability & Statistics are the course's other strand, reasoning about discrete patterns and uncertain outcomes instead of continuous graphs. Every strand here is a runway: asymptotes preview limits, transformations preview derivatives, and series preview integrals — Pre-Calculus and calculus pick up exactly where this course leaves off. Hover any topic to see it highlight — every content unit connects back to Functions. Functions are the language every later unit borrows: a rule pairing each input with exactly one output. Transformations, combining functions, and inverses all trace back to ideas built here in Unit 1. Watch for: a function needs to be one-to-one before it can have an inverse — the horizontal line test decides.

This is the written version of the interactive lesson above. See the full Algebra 2 course.