Algebra & Functions Mind Map

Every algebra & functions visualization on this site on one map. The branches are the main ideas. Each leaf is a page; the grey line under it is the one thing to remember about it. Click a branch to focus on it, click a page to open it.

Recall mode hides the page names. Read the hint, say the name, then click the "?" to check.

1. How the map is organized

Overview of the algebra & functions mind map: Polynomials and graphs, Rational functions, Exponentials and logs, Waves and envelopes, Oscillators, Collisions, Motion under forces, Equations and inequalities. — The map at a glance: 8 branches, 27 pages.

Ask what kind of formula is behind the graph:

Powers of x only? That is a polynomial. If it is divided by another polynomial, it is rational, with asymptotes where the bottom is 0.
Does x sit in the exponent? Then each equal step multiplies: exponentials and logs.
Is there a sine or cosine? A pure formula of a wave is waves and envelopes; a real mass that swings is an oscillator.
Is it a physics problem without a repeat? Objects that hit each other are collisions; anything moved by gravity or friction is motion under forces.

2. The branches side by side

Branch	Typical formula	Key number	Main idea
Polynomials and graphs	ax² + bx + c	b² − 4ac	roots, vertex, turning points
Rational functions	p(x) / q(x)	degree of top vs bottom	asymptotes and holes
Exponentials and logs	a·bˣ + k	doubling time, τ	growth or decay by a factor
Waves and envelopes	g(x)·sin(mx)	frequency m	the envelope bounds the wave
Oscillators	A·cos(ωt + φ)	ω = √(k/m)	period does not depend on amplitude
Collisions	m₁v₁ + m₂v₂ kept	restitution e	momentum kept, energy maybe not
Motion under forces	F = ma	g, μ, GM	split into components

3. Five facts to remember

f(x − h) moves the graph right by h: changes inside the brackets act on x in reverse.
The discriminant b² − 4ac says if a quadratic has 2, 1 or 0 real roots.
An exponential grows by the same factor on every equal step; the log is its inverse.
For small swings, the period of a spring or pendulum does not depend on the amplitude.
Momentum is kept in every collision; kinetic energy is kept only in an elastic one.

See all algebra & functions pages in the index, or the other mind maps.