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Precalculus

Precalculus

Precalculus is the last rung before calculus. It takes the functions introduced in Intermediate Algebra and studies them as objects in their own right — how they transform, compose, and invert — then adds the trigonometry, analytic geometry, and sequence work that calculus assumes, and closes with a first look at limits and derivatives.

This book is being written. Its chapter structure and OpenStax source provenance are pinned, and sections are being published one at a time. Follow the chapter list below to see the planned shape of the book.
Prerequisites: Intermediate Algebra, or comfort with functions, factoring, radicals, quadratics, and exponential and logarithmic functions. This is advisory, not a gate — start here if the earlier material already feels familiar.

Chapters

This book is organized into twelve chapters, each broken into short sections you can work through in order.

  • Functions — function notation, domain and range, rates of change, composition, transformations, absolute value functions, and inverse functions.
  • Linear Functions — linear functions and their graphs, modeling situations with them, and fitting linear models to data.
  • Polynomial and Rational Functions — complex numbers, quadratic and power functions, the graphs and zeros of polynomials, polynomial division, rational and radical functions, and variation.
  • Exponential and Logarithmic Functions — exponential and logarithmic functions and their graphs, the properties of logarithms, solving exponential and logarithmic equations, models, and curve fitting.
  • Trigonometric Functions — angles and their measure, the unit circle definitions of sine and cosine, the other trigonometric functions, and right triangle trigonometry.
  • Periodic Functions — graphs of the sine and cosine functions, graphs of the other trigonometric functions, and the inverse trigonometric functions.
  • Trigonometric Identities and Equations — simplifying and verifying identities, sum and difference identities, double-angle and half-angle formulas, solving trigonometric equations, and modeling.
  • Further Applications of Trigonometry — the Law of Sines and Law of Cosines, polar coordinates and their graphs, the polar form of complex numbers, parametric equations, and vectors.
  • Systems of Equations and Inequalities — linear systems in two and three variables, nonlinear systems, partial fractions, matrices and matrix operations, Gaussian elimination, inverses, and Cramer’s Rule.
  • Analytic Geometry — the ellipse, the hyperbola, and the parabola, rotation of axes, and conic sections in polar coordinates.
  • Sequences, Probability and Counting Theory — sequences and their notations, arithmetic and geometric sequences, series, counting principles, the Binomial Theorem, and probability.
  • Introduction to Calculus — finding limits numerically and graphically, the properties of limits, continuity, and a first look at derivatives.

About this edition

This book is adapted from OpenStax Precalculus 2e, used under the terms of its Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA 4.0) license. Reviewers who vet or adapt this material are credited in the reviewed_by field of each page.

Functions