Precalculus: An Investigation of Functions
David Lippman, Pierce College
Melonie Rasmussen, Pierce College
Conditions of Use
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. read more
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.
The book seems to be very accurate and I did not find any errors while examining the text.
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 I did find one link for source material for a problem that was no longer valid, but this could be easily rectified in a future update.
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.
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.
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.
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.
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.
I did not find any grammatical errors within the text.
I did not find anything within the book that I would view to be culturally insensitive or offensive.
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.
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 read more
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.
All of the problems that I worked, I found to be error-free and unbiased.
All of the applications problems that I read would maintain their relevancy. This text would not need to be updated regularly.
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.
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.
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.
The organization, structure, and flow of this text is very logical and clear.
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.
This text contains no grammatical errors that I found.
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.
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.
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 read more
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.
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.
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.
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.
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.
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.
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.
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.
I did not see any grammatical errors in the text.
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.
It was fun-time reading this book. I thoroughly enjoyed it and may be I will even adopt it in the fall of 2015.
Table of Contents
- Chapter 1: Functions
- Chapter 2: Linear Functions
- Chapter 3: Polynomial and Rational Functions
- Chapter 4: Exponential and Logarithmic Functions
- Chapter 5: Trigonometric Functions of Angles
- Chapter 6: Periodic Functions
- Chapter 7: Trigonometric Equations and Identities
- Chapter 8: Further Applications of Trigonometry
About the Book
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.
About the Contributors
David Lippman received his master’s degree in mathematics from Western Washington University and has been teaching at Pierce College since Fall 2000.
Melonie Rasmussen received her master’s degree in mathematics from Western Washington University and has been teaching at Pierce College since Fall 2002. Prior to this Melonie taught for the Puyallup School district for 6 years after receiving her teaching credentials from Pacific Lutheran University.