Precalculus: An Investigation of Functions

Reviewed by Evgenia Harrison, Instructor, Tidewater Community College on 3/28/23

Comprehensiveness rating: 4 see less

The textbook covers the majority of precalculus and trigonometry topics. It is missing following topics: function arithmetic, point-slope of an equation of a line, systems of linear and non-linear equations, matrices, which you can supplement with a different OER textbook. Otherwise, it provides sufficient explanations and examples for the topics covered. There is an index, and you can use the search option when viewing the PDF files.

Content Accuracy rating: 5

The textbook's content is accurate. There are a few typos, but the textbook comes with an errata.

Relevance/Longevity rating: 5

The textbook provides the basis for calculus classes. The content is up-to-date and includes real life applications and examples. You can download separate chapters as Word documents and easily change or remix them.

Clarity rating: 5

The language of the textbook is easily understandable and uses the proper terminology.

Consistency rating: 5

The text is consistent both concept and style wise. Similar design makes it is easy to navigate each section.

Modularity rating: 5

The text consists of 9 chapters and each chapter consists of 4-8 sections. Each section covers a specific topic and follows the same layout. Everything is clear and visual; the textbook is easy to read and follow.

Organization/Structure/Flow rating: 4

Most of the topics of the text are presented in the learner-friendly order. I would consider teaching a few sections or topics out of order. For instance, graph transformations go before linear functions, inverse functions are covered in two separate sections, trigonometric functions are introduced as ratios in a circle before the text defines them as ratios in a right triangle.

Interface rating: 5

I had no issues with the text's interface. Pictures, graphs, expressions, and text are very clear.

Grammatical Errors rating: 5

I did not notice any grammatical errors.

Cultural Relevance rating: 5

The text is focused on mathematical concepts and their applications. It is not culturally insensitive or offensive.

Reviewed by Naser Al Hasan, Associate Professor, Newberry College on 10/12/22

Comprehensiveness rating: 4 see less

The book covers all the topics typically covered in a Pre-Calculus class. Additionally, the book contains sufficient material for a trigonometry course. There is no review of algebra. Index is very accurate and answers to selected exercises are helpful to students. Front Matter is well written.

Content Accuracy rating: 4

Overall, I found the content to be accurate. Definitions could’ve been stated more precisely then explained in words. Some properties need more clarity, for example when the inverse properties for “logarithms” were introduced on pages 277 (and on 289), restriction on “x” should’ve been included so that students can be reminded of the domain of the composition.

Relevance/Longevity rating: 4

Conceptually is good. Updating applications can be done with ease.

Clarity rating: 4

Overall, the book was clear, and it was written with the students in mind. Many definitions were informal. Trigonometry section did have a very good introduction and good explanations.

Consistency rating: 4

This book is consistent throughout. The authors ensured that a motivation problem is introduced prior to stating definitions. Then the author introduced the necessary definition, some in an informal way, with good examples.

Modularity rating: 4

This book follows the standard set up of any Pre-Calculus course. I found devoting a whole chapter on Linear Functions to be a refreshing concept.

Organization/Structure/Flow rating: 5

The logical flow of topics in this book is the standard flow of topics in any Pre-Calculus book. I did like the learning objectives at the beginning (or within) of each section, such objectives will help students with the mathematical language.

Interface rating: 5

I did not experience any interface issues with this book.

Grammatical Errors rating: 5

I did not see any grammatical errors in the text.

Cultural Relevance rating: 5

The book is culturally neutral.

Comments

This book is informal, intuitive, and straightforward. It was written with students in mind. I would like to see a review of basic algebra. If the instructor is careful to address the places where the book is too informal, I think this book will be a fine Precalculus textbook.

Reviewed by Latha Chakravarthy, Instructor, Central State University on 4/24/19

Comprehensiveness rating: 4 see less

The topics were well addressed, and in particular, the Trigonometry concepts from Chapter 5 onwards were well traversed.

Content Accuracy rating: 5

As such no errors were seen.

Relevance/Longevity rating: 5

Since the books teaches basic concepts with great detail, updates if and when required can be made to questions dealing with applications, in a relatively simple manner. However, conceptually there will be no issues.

Clarity rating: 4

All terminologies and allusions to variables were used in as clear of a form as possible.

Consistency rating: 4

The textbook was consistent throughout.

Modularity rating: 4

I had to especially used Chapters 5-8 from this textbook. I found that there was no problem with the format, and each Chapter could be assigned/worked on individually as long as basic concepts were clear.

Organization/Structure/Flow rating: 5

Very logically and well distributed topics and content. The 'Try it now' questions were very useful, both for me as an instructor as well as for the students.

Interface rating: 4

No issues were found, and students were able to navigate through the content well.

Grammatical Errors rating: 4

No grammatical errors.

Cultural Relevance rating: 5

No such issues were found.

Comments

As an instructor teaching Trigonometry for the first time, I found the textbook extremely useful, and would definitely recommend it to other professors.

Reviewed by Jennifer Fleming, Math Instructor - GED program, Linn-Benton Community College on 2/6/19

Comprehensiveness rating: 4 see less

This book is excellent when it comes to providing students with real-world examples for the topics, but teachers need to be careful when using this book that they define the vocabulary exactly the same as the book does, so as not to confuse the students. . . For example:
Book's definition of a FUNCTION: "A rule for a relationship between an input, or independent, quantity and an output, or dependent, quantity in which each input value determines one output value."
How some teachers define a FUNCTION: "A relationship that shows for every x-value there is one and only one y-value."
These definitions are both saying the same thing, but for a student who is learning it for the first time, such a drastic difference in wording could cause confusion. Here is another example:
Book's definition of RATE OF CHANGE: "Describes how the output quantity changes in relation to the input quantity."
How some teachers define RATE OF CHANGE: "How fast or how slow a function is increasing or decreasing." . . . Be Careful!

Content Accuracy rating: 5

I have used this textbook as an instructor and also as a tutor for many years - I have found no evidence of errors or biased content.

Relevance/Longevity rating: 5

This textbook is very well written and the content is arranged in a way that is most conducive to learning. Within each Section of this book, new vocabulary is defined among several example problems, there is a "List of Important Topics" at the end, and the number of exercises for the students is (for the most part) less than 50 problems so as to make assigning homework easier and less overwhelming / time-consuming.
Also, what makes this textbook somewhat unique and extremely helpful is that it writes out the solutions step-by-step for each of the example problems, and it warns students along the way to "resist the urge" to make common mistakes when solving.
With further regards to relevance, as a teacher, I found it beneficial for my students to teach the entire content of this textbook with the exception of 2 Sections: (5.2) "Linear and Angular Velocity" (skipped because I felt it got too deep into Physics) and (8.5) "Parametric equations; Lissajous figures" (skipped because I felt it to be a bit heavy for Pre-Calculus - better saved for Calculus 1 & 2)

Clarity rating: 4

Some of the definitions for the vocabulary are a bit "wordy" in my opinion, but if students read through them carefully they all make sense and even help answer the ever-popular question, "How am I ever going to use this in the real world?!"
There is just the right amount of Geometry review before the chapters on Trigonometric functions (sine, cosine, etc.), and when students learn how to graph these functions, the book gives the practical example of using these graphs to monitor the changing population of Elk. . . There is never any mention of the acronym, "S-O-H-C-A-H-T-O-A," however, which I highly recommend as I have found to be very useful in helping students understand this section.

Consistency rating: 5

The terminology and topics throughout this textbook are designed in a very consistent framework - each section introduces the material using real-world application examples, shows further examples of how to solve problems step-by-step, introduces new vocabulary where appropriate, gives students a list of topics to review, and then allows for a moderate amount of independent practice.

Modularity rating: 5

Each chapter is divided into several sections, which help break apart the overall topic and allows the teacher to present the material in a way that is neither too fast nor too slow for students to understand. There is even a separate section for allowing students to practice writing Inequalities using Set-Builder and Interval notation - something I've seen other textbooks leave out.

Organization/Structure/Flow rating: 5

Very organized content throughout; Easy to find specific topics and/or example problems.

Interface rating: 5

Many charts, tables, and graphs are used to teach the different mathematical concepts throughout this textbook. I have found them to be essential to the explanations and overall understanding of the topics. Students, in my own experience, have not encountered any issues with how to interpret these images.

Grammatical Errors rating: 5

I have not found there to be any grammatical errors. . . although I am a Math instructor, not an English Language instructor! ;)

Cultural Relevance rating: 5

No offensive or biased references to race, culture, or ethnicity are found among the real-world example problems in this textbook.

Comments

HIGHLY RECOMMEND!!
Excellent resources for students who have completed Algebra 2, and before entering Calculus 1.

Reviewed by Pam Morse, Mathematics Instructor, Columbia Gorge Community College on 12/7/18

Comprehensiveness rating: 4 see less

This textbook covers all areas of a Pre-Calculus Functions book. It includes everything you would need for at least two terms, one of an Intro to Functions and one of Trigonometry. The book is written in an easy to understand format compared to harder texts. There is no review of algebra but the easy to understand textbook with key items in bold and blocked out help.

Content Accuracy rating: 5

I have not found any errors on any of the problems I have worked. The appears to be no bias on any of the problems.

Relevance/Longevity rating: 5

The problems introduces in this textbook are current and relevant to society today. I don't see them needing to be updated or changed in the near future. Students are able to see the relevance for learning the functions.

Clarity rating: 5

This textbook is easy to follow and understand. Any mathematical notation used is explained so that even a "non-math" person can follow. Students should be able to understand the text on their own with little help from an instructor. Terminology is defined also.

Consistency rating: 5

The nice thing about this textbook is that the book follows the same structure for each function defined and talked about in the text. Students are shown problems and answers are given in four methods; verbally, numerically, algebraically, and graphically. So no matter the learning style of the student they have it presented in multiple ways.

Modularity rating: 5

This textbook is set up very nicely. The first four chapters lends itself very nicely to a Functions course. the second half of the text will satisfy and Trigonometry class. The way it is broken up, instructors can use the book in any order.

Organization/Structure/Flow rating: 5

The flow of this book is in a logical manor. The topics appear in an order which will aid the students. Each section of the book has problems worked out for the student and then problems for the student to try along the way. This aids the student to scaffold the information as they go along.

Interface rating: 5

There appeared to be no issues with the navigation of this text book. Links within the book worked seamlessly. I would have liked to see it set up so that it looked like a book with two pages at a time. (That may just have been my browser)

Grammatical Errors rating: 5

I saw no grammatical errors.

Cultural Relevance rating: 5

There was no culturally insensitive or offensive material.

Comments

This book is good introductory book to Functions and Trigonometry. Its ease of reading won't scare students away from the material. It would have been nice though to have a quick algebra refresher. Overall I found it to be well written and set up for easy adoption in a class.

Reviewed by Cristin Barrett, Assistant Professor, Virginia Western Community College on 4/11/17

Comprehensiveness rating: 4 see less

This text covers all areas of a standard Precalculus class, with or without trigonometry. There is no algebra review. There is an effective index and there are solutions to selected exercises in the back. There is no separate glossary, but key terms are in bold and defined within each section.

Content Accuracy rating: 5

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

Relevance/Longevity rating: 5

All of the applications problems that I read would maintain their relevancy. This text would not need to be updated regularly.

Clarity rating: 5

This text is written with excellent clarity. All symbolic notation is clearly explained. This is a text that students would be able to read and follow on their own. Formal notation and terminology is used and are explained very well.

Consistency rating: 5

The book is very consistent in terms of how each function is presented. First, an application is given of how the function is used in modeling. This gives the students an idea of the purpose of each function. Then symbolic notation is introduced for the function, followed by an in-depth study of graphs and modeling. In the Preface, the authors state that the rule of four is used. The functions are all addressed verbally, graphically, numerically, and algebraically. I found this to be true as I reviewed each one.

Modularity rating: 4

Each section is an appropriate length. Examples and definitions are clearly labeled. The text could easily be used for a Precalculus without trigonometry class and a Precalculus with trigonometry class. No algebra review is given, nor are there any appendices on algebra topics.

Organization/Structure/Flow rating: 5

The organization, structure, and flow of this text is very logical and clear.

Interface rating: 4

This text is easy to navigate. The table of contents is useful and the page headers are as well. However, I did find that the symbol for the set of real numbers did not get printed on page 23. This is the only distortion/display issue that I came across.

Grammatical Errors rating: 5

This text contains no grammatical errors that I found.

Cultural Relevance rating: 5

The examples and exercises in this book apply the mathematics to a wide variety of scenarios. None of them appear to be culturally insensitive or offensive.

Comments

The only thing I would like to see added to this text would be a basic algebra review, or some appendices on algebra that students could use to brush up on pre-requisite skills if necessary. I also would like to see an introduction to the difference quotient. Otherwise, I thought this was an excellent Precalculus text.

Reviewed by Amanda Copeland, Adjunct Professor, Virginia Western Community College on 4/11/17

Comprehensiveness rating: 4 see less

This book is very thorough in the topics that are covered and seems to contain nearly everything that I would expect to find in a precalculus course. The only topics that I wish were included is finding oblique asymptotes and solving for complex zeroes, however I think that it would be very simple to add a supplementary resource for those topics.

Content Accuracy rating: 5

The book seems to be very accurate and I did not find any errors while examining the text.

Relevance/Longevity rating: 5

In my opinion the book has current applications and will remain relevant for a long time. I did find one link for source material for a problem that was no longer valid, but this could be easily rectified in a future update.

Clarity rating: 5

This text was written very clearly using correct terminology. This is a good source for students to use in learning precalculus, but due to that fact that many students have difficulty reading math texts they may have to read a section more than once to fully grasp a concept.

Consistency rating: 5

The book has a very consistent lay out and even color codes different features. For example, blue headings are for concepts and definitions, grey headings are for worked out examples and green headings are problems for students to try.

Modularity rating: 5

The book has chapters that focus on broad topics and each chapter is subdivided into more specific concepts allowing for the instructor to easily organize for specific lessons.

Organization/Structure/Flow rating: 5

The organization and order for the presentation of material seems to be in a logical order. What I really enjoy is that within each section the text has worked out examples for the student to learn from and then has a similar problem for the student to try with answers to the try it problems at the end of the section.

Interface rating: 5

When I went through the book all of the images were clear and I did not have any navigational issues. I do recommend viewing the book in a two page book layout because the margins are set up for it to be a book. If you do not view it in a two page book layout it does not negatively effect anything, the reader will just notice that the margins change every page.

Grammatical Errors rating: 5

I did not find any grammatical errors within the text.

Cultural Relevance rating: 5

I did not find anything within the book that I would view to be culturally insensitive or offensive.

Comments

I think that this is a really well written book that has some really interesting practice problems and applications. One thing that I really appreciated was the fact that the book had links for resources that could be used with it. For example, there was a link to a web-based linear regression calculator for students to use. This is definitely a book that I will consider adoption for my future precalculus courses.

Reviewed by Joyati Debnath, Full Professor, Winona State University on 6/10/15

Comprehensiveness rating: 5 see less

The book covered all the topics that any instructor might want to cover in one or two-semester long in a college level Pre-Calculus course. It has 12 chapters and is divided into 3 groups. First group is the first 4 chapters that cover functions creating a solid foundation for the course. Second is all about Trigonometry and its applications. I appreciate the way it began this section using angles and unit circles and then moving on to triangles. Third piece is dealt with the advanced topics with systems and equations, a little of discrete math, analytic geometry and a prep for calculus. Interestingly, this is exactly how I teach the course and divide the semester with the content of the course. I loved the figures and illustrations that used contemporary styles with color contrast and labeling.

Content Accuracy rating: 5

It seems like authors have taken a great effort to ensure the validity and accuracy of the content in the book. Each chapter’s manuscript underwent at least two rounds of review and revision by a panel of active Precalculus instructors. Another team of experts checked all text, examples, and graphics for mathematical accuracy. A third team of experts tested the accuracy of the Answer Key, by re-working every solution. The Solutions Manual was rigorously checked for accuracy.

Relevance/Longevity rating: 5

The content of the book seems to be very contemporary and up-to-date. It used very relevant real-life problems and examples. It added media buttons that can be changed or updated if necessary. At the end of every chapter the access to online resources are very useful.

Clarity rating: 5

The authors used clear concise English language without any redundancy. It clearly says what it is planning to do every step and showed detailed work in the examples. It also added analysis that musty be very helpful to the students. The graphs shown are just like I would do in class on the board. All the explanations used “we” that is very appropriate for the students to see the line of thinking within the mind of the author.

Consistency rating: 5

The format is very consistent with mathematical languages and terminology. It appears that the authors have used their own text repeatedly and they have done a good job providing links to the online sources. The figure for vertical and horizontal reflection is beautifully done. This is true for all mathematical concepts. The figures are very valuable learning component for the students to see and are consistent with the topics. It used very appropriate standard mathematical terminology throughout.

Modularity rating: 5

The book used standard sequence of topics. It can easily be divided in two semester long courses if needed. In some schools advanced topics are not covered in PreCalculus courses and hence these topics can be avoided without any trouble.

Organization/Structure/Flow rating: 5

The organization/structure/flow of this book is outstanding with learning objectives at the beginning of every section. This helps the instructors to clearly focus on the topics and techniques.

Interface rating: 5

I did not experience any interface issues with this text. The links within the text, takes the reader to statements of previous theorems, previous examples, particular exercises, a referenced diagram, definition, or solution of an exercise, which is a handy feature. At the end of every chapter the key concepts quickly links to the topic discussed in the sections.

Grammatical Errors rating: 5

I did not see any grammatical errors in the text.

Cultural Relevance rating: 5

The book seemed to be culturally neutral. I did not notice any race or religion based problems. The problems used “you” or “your” many times. Other problems centered on the mathematical concepts.

Comments

It was fun-time reading this book. I thoroughly enjoyed it and may be I will even adopt it in the fall of 2015.