MAC1140

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 revisited 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 WAMAP.org template course list. For those located elsewhere, you can access the course shell at MyOpenMath.com. A self-study version of the online course exercises is also available on MyOpenMath.com for students wanting to learn the material on their own, or who need a refresher.

Precalculus 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical precalculus course. The text proceeds from functions through trigonometry and ends with an introduction to calculus. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Precalculus 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

The Precalculus 2e revision focused on improving relevance and representation as well as mathematical clarity and accuracy. Introductory narratives, examples, and problems were reviewed and revised using a diversity, equity, and inclusion framework. Many contexts, scenarios, and images have been changed to become even more relevant to students’ lives and interests. To maintain our commitment to accuracy and precision, examples, exercises, and solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates from the first edition were considered and unified across the different formats of the text. The first edition of Precalculus by OpenStax is available in web view here.

This Grants Collection for College Algebra, Trigonometry, and Precalculus was created under a Round Five ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Topics in Precalculus is a compilation of ideas and concepts designed to prepare you for the study of Calculus. In addition to re-enforcing content from algebra such as exponential and logarithmic functions, and complex numbers, this book introduces the reader to more novel concepts by investigating in detail two of the most basic shapes in geometry: the circle and the triangle. Join us as we explore this ancient subject that extends our knowledge of these shapes by explaining them in terms of trigonometry. In fact, our study of the six trigonometric functions will allow us to apply the relationships described in precalculus to other branches of science such as physics and astronomy. The connections revealed between both the new and familiar ideas described in Topics in Precalculus will assist you with your mathematics journey in a book that’s designed just for YOU!

Precalculus is an introductory text. The material is presented at a level intended to prepare students for calculus while also giving them relevant mathematical skills that can be used in other classes.


The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the mathematics, not to replace it.