Precalculus

Functions, logs, trig, sequences, and limits — the toolkit you need before calculus makes sense.

Function Basics — Domain, range, and injective / surjective / bijective — the language of functions.
Function Composition & Inverse — (f g)(x) = f(g(x)), and f^-1 undoes f — a reflection across y = x.
Inverse Functions (2) — f^-1 undoes f. Swap x and y, solve for y.
Logarithm Rules — A log is an exponent, so the log laws are the exponent laws backwards: _b(ac) = _b a + _b c, and friends.
Log Change of Base — _b(x) = _c(x)/ _c(b) — switch to a base where you can see the answer.
Radians & the Unit Circle — An angle is how much arc it cuts: 180^ = π radians.
Trig Functions — , , from two pictures — right-triangle (SOH-CAH-TOA) and unit-circle ( θ, θ).
Trig Values — , , at 0, π/6, π/4, π/3, π/2 — the unit circle by heart.
Trig Identities — ^2θ + ^2θ = 1 — and the even/odd symmetries.
Law of Cosines — c^2 = a^2 + b^2 - 2ab C — Pythagoras with a correction term.
Law of Sines — a/ A = b/ B = c/ C — sides scale with the sines of their opposite angles.
Sequences & Series — ∑ notation and the closed forms: _i=1^n i = n(n+1)2 and geometric _k r^k = r^n-1r-1.
Limits — Factor, cancel, plug in — the 0/0 recipe.
Limits at Infinity — End behavior, horizontal asymptotes, and one-sided limits.

Further Topics

Graph Transformations — Shifts, reflections, and stretches read off a parent graph.
Polynomial Functions & Graphs — Zeros, multiplicity, and end behavior from the formula.
Rational Functions & Asymptotes — Vertical, horizontal, and slant asymptotes from a quotient of polynomials.
Exponential Functions & Equations — Growth and decay with a b^x, and solving a b^x = c with logs.
Conic Sections — Standard forms of the parabola, ellipse, and hyperbola.
Polar Coordinates — Locate points by radius and angle, and convert to and from rectangular form.
Vectors (2D) — Components, magnitude, and the dot product in the plane.