Precalculus: An Investigation of Functions (2nd Ed)

David Lippman and Melonie Rasmussen

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisted more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation.

In addition to the paper homework sets, algorithmically generated online homework is available as part of a complete course shell package, which also includes a sample syllabus, teacher notes with lecture examples, sample quizzes and exams, printable classwork sheets and handouts, and chapter review problems. If you teach in Washington State, you can find the course shell in the template course list. For those located elsewhere, you can access the course shell at A self-study version of the online course exercises is also available on for students wanting to learn the material on their own, or who need a refresher.

The whole book or individual chapters are available for download below, or you can order a bound printed copy from, Createspace, or Amazon. If you are providing a link to students or a bookstore to purchase printed copies of the book, please direct them to this page. If you are an instructor and are using this book with your class, please drop us an email so we can track use and keep you updated with changes.

Errata (errors). Any errors reported will be cataloged here.

ContentsBookDetailed Solutions
Whole Book - 2nd Edition PDF
Order full book from Lulu
Chp 1-4: PDF, Lulu or Amazon
Chp 5-9: PDF, Lulu or Amazon
Front Matter PDF DOCX
Chapter 1: Functions
  • 1.1 Functions and Function Notation
  • 1.2 Domain and Range
  • 1.3 Rates of Change and Behavior of Graphs
  • 1.4 Composition of Functions
  • 1.5 Transformation of Functions
  • 1.6 Inverse Functions
Chapter 2: Linear Functions
  • 2.1 Linear Functions
  • 2.2 Graphs of Linear Functions
  • 2.3 Modeling with Linear Functions
  • 2.4 Fitting Linear Models to Data
  • 2.5 Absolute Value Functions
Chapter 3: Polynomial and Rational Functions
  • 3.1 Power Functions & Polynomial Functions
  • 3.2 Quadratic Functions
  • 3.3 Graphs of Polynomial Functions
  • 3.4 Factor and Remainder Theorem
  • 3.5 Real Zeros of Polynomials
  • 3.6 Complex Zeros
  • 3.7 Rational Functions
  • 3.8 Inverses and Radical Functions
Chapter 4: Exponential and Logarithmic Functions
  • 4.1 Exponential Functions
  • 4.2 Graphs of Exponential Functions
  • 4.3 Logarithmic Functions
  • 4.4 Logarithmic Properties
  • 4.5 Graphs of Logarithmic Functions
  • 4.6 Exponential and Logarithmic Models
  • 4.7 Fitting Exponentials to Data
Chapter 5: Trigonometric Functions of Angles
  • 5.1 Circles
  • 5.2 Angles
  • 5.3 Points on Circles using Sine and Cosine
  • 5.4 The Other Trigonometric Functions
  • 5.5 Right Triangle Trigonometry
Chapter 6: Periodic Functions
  • 6.1 Sinusoidal Graphs
  • 6.2 Graphs of the Other Trig Functions
  • 6.3 Inverse Trig Functions
  • 6.4 Solving Trig Equations
  • 6.5 Modeling with Trigonometric Equations
Chapter 7: Trigonometric Equations and Identities
  • 7.1 Solving Trigonometric Equations with Identities
  • 7.2 Addition and Subtraction Identities
  • 7.3 Double Angle Identities
  • 7.4 Modeling Changing Amplitude and Midline
Chapter 8: Further Applications of Trigonometry
  • 8.1 Non-right Triangles: Law of Sines and Cosines
  • 8.2 Polar Coordinates
  • 8.3 Polar Form of Complex Numbers
  • 8.4 Vectors
  • 8.5 Dot Product
  • 8.6 Parametric Equations
Chapter 9: Conics
  • 9.1 Ellipses
  • 9.2 Hyperbolas
  • 9.3 Parabols and Non-Linear Systems
  • 9.4 Conics in Polar Coordinates
Answers to Selected Exercises PDF DOCX

Text last updated: August 2020. Latest Edition: 2.2. The PDF links and Amazon print links are edition 2.2. The Lulu print links are still for edition 2.1, as they've raised their printing prices on new books higher than we're willing to charge, so are looking into new options.

Creative Commons License
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.

The detailed solutions manual was contributed by Shoreline Community College and Evergreen State College, and is licensed under a Creative Commons Attribution-NonCommercial ShareAlike License.

Note on versions: The links above will redirect you to the latest edition of the chapters. Older versions remain on the website, and can be accessed using direct links to the specific edition's file name, like 1.pdf

Note: On June 5, 2017, Edition 2.0 was released. The links below point to this, the most current version. This revision is not page number or section equivalent to the previous 1.x editions. If you are looking for the original first edition (black cover), please go here

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