# Precalculus

Jay Abramson, Tempe, Arizona

Valeree Falduto, Lake Worth, Florida

Rachael Grosss, Towson, Maryland

Copyright Year: 2014

ISBN 13: 9781938168345

Publisher: OpenStax

Language: English

## Formats Available

## Conditions of Use

Attribution

CC BY

## Reviews

The topics covered are standard in state articulation guides, for example, the 2019 Illinois Mathematics & Computer Science Articulation Guide. See the topics covered under "Elementary Functions (Precalculus)" which refers back to the tables... read more

The topics covered are standard in state articulation guides, for example, the 2019 Illinois Mathematics & Computer Science Articulation Guide. See the topics covered under "Elementary Functions (Precalculus)" which refers back to the tables of contents for College Algebra and Trigonometry. Therefore this text is very suitable for helping two-year community college students articulate with the third year at a four-year public university's Calculus I course. It is also compatible with a private university's precalculus and later calculus sequence.

The text is mathematically correct and complete. Its rigor is communicated clearly and simply, even "conversationally," to all students, but is suitable for STEM majors as well.

The actual mathematical content as such should not change much. However, mathematical modeling problems ("story problems," "applications") are in a variety that represent daily adult life, post-college careers, various majors other than mathematics such as science, health, ecology, and medicine for example. These examples are fairly applicable in a non-dated, but modern vein.

It is a text which students can learn from in its simplicity, clarity, and logic, and conversational tone, while maintaining mathematical correctness and completeness.

An important element of consistency is how well a text develops topics in a developmental sequence that builds from topic to topic. This text has a good topic sequencing in that fashion.

It can be organized in modules as long as necessary topic sequencing is maintained. For example, jumping into the topic in vectors concerning the angle between two vectors should honor the necessary trigonometry needed to built that topic upon. There are appropriate subheadings to signal the student as to the organization and connections being made under a new subheading with previous subheaded topics.

This is topic sequencing, and I have mentioned that this text maintains a logical, developmental topic sequencing structure. I've mentioned its simple and clear explanations while maintaining mathematical accuracy and completeness.

In my opinions diagrams and charts are well-placed and referenced as needed in text discussions of a topic.

I have taught the trigonometry portion of this text, which is in Chapters 5-8, and a portion of introductory calculus in Chapter 12, and found no such errors.

I did not detect any distracting or blatant biases in any examples or discussions of any "culturally insensitive" or "offensive" nature at all, or in the nature of any social or ethnic exclusiveness of any kind.

Whenever I have reviewed either new textbooks or revisions of current textbooks for remuneration by a publisher, I have followed my practice of looking for the following for strengths or weaknesses. I ask if the text: 1. is mathematically complete and accurate, 2. teaches clearly, simply, and logically so that a student can learn from studying it, 3. has good problems in the exercises and discussion examples, and 4. has good end materials for review and test practice, 5. has computational skills balanced with applications (i.e. both procedural skills with applications which are connected to discussion topics and require practicing the skills and knowledges learned for the procedural skills). This text has all five. I have enjoyed teaching with it and helping students through reading and learning from the text as well.

Overall very good selection of topics, coherent, includes many engaging visual features and excellent real world applications. read more

Overall very good selection of topics, coherent, includes many engaging visual features and excellent real world applications.

Accurate. I did not find any errors.

Definitely good up-to-date applications and approaches. The text is written in a way that the updates will be easy to implement if necessary.

Very clear writing style. Formal when necessary and good examples and illustrations to make concepts more accessible for the students.

The text is consistent throughout. The content is well organized, presented in a coherent way. Terminology is consistent.

This text is designed to be modularized. Most Precalculus courses will not cover all of the topics from this text but will cover a subset of these and the text is written with the goal to accommodate that. Rearranging the order of topics could be an issue because of the hierarchical structure of mathematics in general.

The text is organized in a way that I would structure my own Precalculus course. Topics are presented in a logical and clear fashion.

I did not find any navigation problems or issues with visual features. The material flows smoothly and the presentation is very user friendly.

I did not find any grammatical errors.

Examples are inclusive and carefully chosen. I did not see anything that could be offensive in any way.

Very good overall. As I mentioned above, this book probably has more than most of us can fit into our typical Precalculus course but it is certainly not missing anything and could be easily customized.

I used Sullivan's Calculus (9e) as a standard for comparisons. The book is very similar in scope and sequencing to Sullivan, but does group some topics differently. For example, Sullivan combines linear and quadratic functions into one short... read more

I used Sullivan's Calculus (9e) as a standard for comparisons. The book is very similar in scope and sequencing to Sullivan, but does group some topics differently. For example, Sullivan combines linear and quadratic functions into one short chapter while this text dedicates a long chapter solely to linear functions and uses that space to develop them more coherently. Sullivan pulls together some topics into an appendix as a review while this text does not. However, this text develops much of that material in context, which I prefer. Both give a brief, but useful few pages of formulas, identities, and standard functions. Each chapter reviews key-concepts and has a glossary of terms. There is an index which seems adequate though it is considerably smaller than Sullivan's.

I saw nothing that would make me doubt the accuracy of the material. The text lists about 50 credentialed content reviewers including faculty and teachers. Problem solutions seem accurate and well developed.

This text is a standard presentation of the material drawing references from travel by car, psychology, engineering, biology, physics, and economics, which seems typical. It would be nice to see more application in computer programming and data analysis and to simulations. There is nothing faddish about its content or presentation. A few cultural references may become dated but could easily be updated as they are isolated and not threaded through the material.

This text uses standard academic English, but seems less formal than Sullivan. For example, it avoids archaic constructions like "we first develop", "we first look at", and "let us investigate", which I find stultifying in Sullivan. It is well written and lucid and takes space, I feel, to develop material more naturally than Sullivan. For example, it develops the techniques for graphing and analyzing linear equations in context rather than in an appendix. For another, it introduces complex numbers in the context of polynomial functions, a natural place, by discussing the way mathematics has grown, while Sullivan introduces the topic ad hoc as an example of using rectilinear and polar coordinates but refers students to an appendix, with a more formal presentation.

The text develops the standard terminology around functions, models, and graphing consistently. Technical terms are introduced in boldface in the body of the text and then defined more formally in easy to locate text-boxes. It introduces standard notations well and uses them consistently. Each chapter presents a glossary with give brief, well written definitions and key concepts, and the concepts include clickable links back to examples in the text.

Chapters are broken into from four to ten sections of about 10 to 20 pages. Sections are largely self-contained and could be used to supplement other coursework. For example, I could see the sections introducing linear functions or the unit circle being used as a review elsewhere. Sections are further divided into two sub-levels that are easily scanned. The development of a topic seldom goes for more than a page without a worked example and a sample problem with the solution presented later.

The material is presented logically and laid out well. This text tends to develop topics in context and avoids putting basic into an appendix.

There are two digital versions: a downloadable PDF and an HTML version accessible online. The PDF is also available printed from OpenStax for a fee. The PDF is nicely laid out to professional standards and displays well on a tablet. It offers a table of contents, full-text searching, and clickable links to examples, solutions, section headings, and to online-videos on some topics. Solutions to selected exercises and "try it" problems are collected at the back of the PDF, as is standard for print editions. The online, HTML, version is less readable. It uses clunky grey boxes to organize in-text features, cluttering the flow of the material. It has the clickable links of the PDF, but pages, examples, and the exercises are not numbered and are not tied well to the PDF version. Graphs are larger online and can be zoomed in using the browser interface. Formulas are rendered via MathJax and can be set to zoom as well. Solutions to selected exercises and "try it" problems are available from a button under the problems. Overall, the typography and design of the PDF version is cleaner, easier to scan, and similar to most professional textbooks, while the online version, though clear and readable, is clunkier, harder to scan, and lacks key labels like page numbers and example numbers, and most distressing, the exercises are not numbered. The PDF seems well suited as a stand-in for a printed text, while the HTML seems best suited as a quick, linkable reference for online homework platforms like WebAssign.

The language and style is mildly formal academic English. It flows well and less formal than some, making it, I believe, more likely to be used by students for learning.

There was nothing I imagined would be offensive to people broadly, but the cultural roots of the text are in American middle-class society: place names such as California, Florida, and New York City are used without reference to the country, though other countries are referenced, especially in photographs. Practical problems use dollars, gallons, and miles, though international standard units are used appropriately in science and engineering contexts. Common names are more often White American, though there is some variety. Situations were mostly urban and academic and would be familiar to White America. Most examples avoid gender by referring to people by their role (scientists, hikers, etc.), but when gender is mentioned, agency and expertise is attributed to males and females.

I used Sullivan' Precalculus (9e) as a standard for comparison. This book holds up well. In fact, I prefer the flow of the content and the naturalness of the development. The PDF is a good stand-in for a printed book. Cengage's WebAssign supports this text. I recommend it as a completely functional text for a serious pre-calculus course.

The textbook covers all standard area and ideas for a Precalculus course. It also provides some advanced contents that are linked to Calculus. A review of basic algebra contents at the beginning of the text could have added good flavor to the... read more

The textbook covers all standard area and ideas for a Precalculus course. It also provides some advanced contents that are linked to Calculus. A review of basic algebra contents at the beginning of the text could have added good flavor to the textbook. In general, the textbook is a comprehensive one that gives instructors flexibility to choose from for a semester course.

All of the chapters that I reviewed and problems that I worked, I found to be error-free and unbiased.

I found most of the application problems that I read relevant. I believe it will remain relevant for a long time.

The text was written lucidly using accurate terminology. At the end of each chapter, the text provides definitions to key terminologies, which makes easy to access for students.

Each section and each chapter has consistent design that simplify the usage of the book. Each section started with a summary that gives a glimpse picture of the main idea of the section before delving into the detailed idea of the section. Then followed by key equations, key notes, exercise, and glossary of the section. In addition, the book suggests access to online resources for additional instruction and practice with topic of each section.

The chapters in the book are subdivided into more specific sections, and each section also provides full concepts for the topic under each section. This consistent lay out allows instructors to easily re-order the chapters and topics according to their needs.

The chapters and sections of the book is well organized and designed in a comprehensible manner. Topics in each chapter and section has consistent lay out, which makes easy to navigate. In addition, the PDF file suitably displays colorfully the different topics and titles of each chapter.

The interface of the book is great. I found out that all the images are clear. I do recommend viewing the PDF file of the book as it links the index to appropriate page in the text easily. In addition, in the review section of each chapter, the specific example that goes with specific topic is appropriately linked, which makes it easy to navigate.

I did not find any grammatical error in the text.

All of the examples and problems I reviewed are culture and gender neutral. I did not find anything that I would be considered culturally insensitive or offensive.

The fact that this book has all the necessary topics and concepts that anyone would look for a precalculus course, and the fact that it is well organized with superb interface features, it is definitely a book that I would consider adopting for my future precalculus course.

It seems to cover all topics of Precalculus and also covers some preview of Calculus. However, the text does not cover review of Algebra. If it also covers a little bit of reviews such as basic factoring and other topics from Algebra, then it... read more

It seems to cover all topics of Precalculus and also covers some preview of Calculus. However, the text does not cover review of Algebra. If it also covers a little bit of reviews such as basic factoring and other topics from Algebra, then it would be better.

I have not found any error/mistake except one minor one. On p.386, Example #11 contains an error in the solution. I am guessing that the author originally intended to have an example with two minuses but included typos.

Due to the nature of the topic, I cannot consider any such issues.

Most of parts are very clearly explained (including a lot of graphs for visualization of the concepts).

Yes.

Due to the nature of the topic, I do not think this question is relevant to this textbook (most of the concepts must be build up based on other concepts).

Yes.

I have not found any interface issues yet.

I have not found any grammatical error yet.

I have not found any parts that are culturally insensitive or offensive in any way.

The textbooks is well organized and written. I do not expect any problem to use this textbook as the main textbook of my Precalculus class.

More important than the generous selection of topics that this text includes is the inviting way in which the mathematics is presented, through engaging and colorful pictures, tables, graphs, and examples from real life (for example, in... read more

More important than the generous selection of topics that this text includes is the inviting way in which the mathematics is presented, through engaging and colorful pictures, tables, graphs, and examples from real life (for example, in introducing logarithms via application to the Richter scale). The engaging style is essential to building an understanding that is comprehensive not only in breadth of topics but also in its relevance, interest and hands-on feel for the student.

The text is accurate, in as much as I have read.

The mathematics is classical, but presented in a modern-day setting that includes examples and motivation from current and recent events; these will be both easy to update and interesting for years to come.

The concepts are presented without clutter, in a friendly yet accurate way. The "Q&A" questions and answers add to the interactive feel. In places, some formalism seeps in, but this is dispelled by clear pictures and examples and practice questions for the student to try. The "How To" boxes are generally helpful, but at times they reduce creative thinking to an algorithm without ample explanation for why it works (as for example, in finding the vertex of a quadratic function). Here the instructor will need to fill in the reasoning, letting the text serve as a reference and summary. The real-world applications help make the mathematics more clear.

The text is consistent in both terminology and style.

The text is conveniently divided into smaller sections that can be easily located and studied at any point in the course.

The organization of the topics and the ideas within each topic follows a logical succession, while the modularity allows for any sub-topic to be studied with as much independence as possible.

The interface is uncluttered and easy to navigate. I have not had the opportunity to use this book yet, but my impression is that the students (and I) would find it easy and enjoyable to work with.

The grammar is good.

The examples are varied, from modern everyday life, and they come across as truly relevant (rather than contrived). At least one (about movies) I thought was insensitive, but there are plenty of good examples in the text.

I imagine that students will enjoy reading this book because of its friendly, interactive, example-oriented, uncluttered, and easy-to-navigate style. This is a book that I can see as a truly helpful learning companion.

## Table of Contents

- 1 Functions
- 2 Linear Functions
- 3 Polynomial and Rational Functions
- 4 Exponential and Logarithmic Function
- 5 Trigonometric Functions
- 6 Periodic Functions
- 7 Trigonometric Identities and Equations
- 8 Further Applications of Trigonometry
- 9 Systems of Equations and Inequalities
- 10 Analytic Geometry
- 11 Sequences, Probability and Counting Theory
- 12 Introduction to Calculus

## Ancillary Material

## About the Book

*Precalculus *is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing College Algebra and Algebra and Trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses.

OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.

## About the Contributors

### Authors

**Lead Author, Senior Content Expert**

**Jay Abramson**, Arizona State University

**Authors**

**Valeree Falduto**, Palm Beach State College

**Rachael Grosss**, Towson State University