A free OpenStax college precalculus textbook covering functions, linear/polynomial/rational/exponential/logarithmic functions, the trigonometric functions, identities and equations, further trigonometry applications (incl. polar/parametric/vectors), systems of equations and matrices, analytic geometry (conics), sequences/probability/counting, and a brief introduction to calculus (limits, continuity, derivatives).
Foundations of functions: notation, domain/range, rates of change, composition, transformations, absolute-value functions, and inverses.
Linear functions, their graphs, modeling with linear functions, and fitting linear regression models to data.
Complex numbers; quadratic, power, polynomial, and rational functions; division of polynomials; zeros; inverses and radical functions; modeling with variation.
Exponential and logarithmic functions and their graphs, properties of logarithms, equations, models, and curve-fitting.
Angles, the unit circle, sine and cosine, the other trigonometric functions, and right-triangle trigonometry.
Graphs of the trigonometric functions and inverse trigonometric functions.
Verifying identities, sum/difference, double-angle/half-angle/reduction formulas, product-to-sum/sum-to-product, solving equations, and modeling with trig functions.
Non-right triangles (Laws of Sines and Cosines), polar coordinates and graphs, polar form of complex numbers, and vectors.
Linear and nonlinear systems of equations and inequalities; matrices; solving with Gaussian elimination, inverses, and Cramer's Rule.
Conic sections in standard form (ellipse, hyperbola, parabola).
Arithmetic and geometric sequences and series, summation notation, and the binomial theorem.
Limits via tables, graphs, and properties; continuity; derivatives. A brief preview of single-variable calculus.