Precalculus: An Investigation of Functions

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, algorithmetically 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 or 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 in the 1st edition). Many of these errors have been corrected in Edition 1.5.

Note: On July 3, 2015, Edition 1.5 was released. The links below point to this, the most current version. This edition is page number and problem set number equivalent to Edition 1.0 - 1.4; it features error and typo corrections.

ContentsTraditional BookDetailed Solutions
Whole Book PDF
Order from CreateSpace
Order from Lulu
Order from Amazon
Front Matter PDF DOC PDF DOC
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 Rational Functions
  • 3.5 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 Parametric Equations
Answers to Selected Exercises PDF DOC
Alternate Extended 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
This alternate chapter contains content remixed from Precalculus by Stitz and Zeager.
This chapter is not included in the standard print version.
There is a full book PDF including the extended chapter, and it is available in print via Lulu.

Text last updated: July 3, 2015. Solutions updated: April 20, 2015

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: The "Split book" version of the book has been phased out due to lack of interest.

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

Locations of visitors to this page