# College Algebra

Multiple Authors , Openstax College

Pub Date: 2015

ISBN 13: 978-1-9381683-8-3

Publisher: OpenStax

## Conditions of Use

Attribution

CC BY

This textbook covers all topics in college algebra, with many chapters to review pre-requisite knowledge, including solving linear equations, … read more

This textbook covers all topics in college algebra, with many chapters to review pre-requisite knowledge, including solving linear equations, factoring, solving quadratic equations and graphing quadratic functions. Instructors who have a need to review pre-requisite knowledge can find useful resources in this textbook. The online version’s lesson index can be toggled. This is a great feature. The PDF version's lesson index are all hyperlinks to the corresponding lessons.

I didn't find any grammar or math errors.

Each lesson starts with a real-life application. The textbook uses many real-live scenarios in examples. However, in each lesson’s exercises, there are usually fewer than 5 application problems. There should be more. Technology content is written for TI-83/84, an outdated model. The textbook should instead use Desmos or Geogebra, free resources for students.

The textbook's language is easy to understand. For some difficult topics, the textbook can be confusing for students who are not used to reading math textbooks. This is a common issue for all math textbooks, though. It's difficult for students to read through textbooks in general.

I didn't find any consistency issues.

The textbook is easily and readily divisible into smaller reading sections that can be assigned at different points within the course. Each lesson's objective is clear.

Lessons are organized into a logical order, with later lessons built on earlier lessons. Functions are introduced early on.

The following are some good features: Important procedures and strategies are summarized in grey boxes. The textbook’s online version has solutions which can be toggled. The PDF version has hyperlinks to figures and tables. Both the online version and the PDF version have hyperlinks to Youtube videos. At the end of each chapter, key concepts are listed with hyperlinks to corresponding examples. The textbook needs improvement in the following aspects: The textbook’s online version has errors in figure referencing. Instead of saying “Figure 1.2 shows …”, it says “Figure shows …”. The PDF version doesn’t have this issue. This is a serious issue affecting students’ reading. In the online version’s exercises, only odd-numbered solutions are shown. This is very confusing to students. They are looking at two problems, but only one solution is available, and it’s not clear which problem’s solution they are looking at. Before this is fixed, it’s hard to use the textbook’s exercises in the online version. The PDF version doesn’t have this problem. The online version supports search of key words. However, when I search for phrases by using quotation marks, it found some extra results which have only a part of the phrases. The textbook has a way to receive feedback (reporting errors), but the link to report error is not available when you are reading the textbook. You have to open a new tab, go to the textbook’s homepage to find the link. Once I click on it, I need to sign up to report an error, and the error form gives me an error when I use Safari. The error doesn’t happen when I switch to Chrome. This process should be made easier. Any reader should be able to report an error.

I found no grammar mistakes.

This textbook has little mentioning of any cultural issues. I didn't found examples using names.

The textbook covers regression for linear, exponential and logarithm functions, but not for polynomial functions. At least it should cover modeling with quadratic functions, a common application in real life. Before the following issues are resolved, it's hard for me to use it in my classes: 1. TI-83/84 examples should be replaced by Desmos/GeoGebra examples. 2. The online version should either show solutions to all exercises, or remove even-numbered exercises. 3. The online version should add numbers to hyperlinks to figures and tables. Instead of saying "Please look at Figure", it should say "Please look at Figure 1".

College Algebra includes all the topics critical to a college algebra course, including review topics. It is complete in its coverage of the building … read more

College Algebra includes all the topics critical to a college algebra course, including review topics. It is complete in its coverage of the building blocks of algebra, many types of functions, their graphs and conic sections. The exercise sets include sufficient variety and quantity of exercises to practice the ideas and skills covered in each section.

There have been some inaccurate labels and directions in the PDF version that I have not seen in the online version.

Overall the text includes applications ranging across many subjects, issues, fields, and interests to be meaningful to a wide cross section of students. And the examples and exercises are generic and basic enough that they will not be out of date.

The textbook introduces new concepts and notation in each section with clear explanation. Sections present concepts in a variety of ways from paragraph explanation, to boxed definitions and results, to “How to” boxes and “Q&A” each providing differing facet of the content and level of detail. Pictures, tables, graphs and other visuals effectively illustrate ideas in a clear manner.

The text is consistent in layout and approach to topics. Terminology is used in a consistent way throughout the chapters.

Sections within each chapter break up the material such that it can be covered in a single class session. (One exception to this is 2.2 Linear Equations in One Variable which covers solving linear equations and finding and graphing linear equations. The latter is also included in 4.1 Linear Functions). The content in the sections is divided into self-contained topics which allows for easy reference or for reordering (or skipping) to serve overall course objectives.

Overall the text is organized such that concepts build on each other in a logical fashion. However, I have also found that covering 2.1 The Rectangular Coordinate Systems and Graphs right before chapter 3 on Functions works well too, as does covering 3.7 Inverse Functions, before Chapter 6 on Exponential and Logarithmic Functions. Within chapters, sections move back and forth between explanation, examples, “how to” pull outs, summary boxes, also in a logical sequence, addressing key points as appropriate to the flow of the text.

The interface for both the PDF and the online version work well and navigating around the text with the table of contents is convenient. The PDF version has numbers on the section exercises whereas the online version has links to selected solutions but does not have exercises numbers, which can be confusing.

I have not found any grammatical errors in the text book.

I have not come across anything in the text that raises concerns or questions related to cultural relevance.

I have used several textbooks for college algebra and find this textbook to be just as good or better than ones with high price tags, so being free to students makes it a good choice. I will likely continue to use this textbook.

The college algebra text covers all the typical topics for a course of this type. Within each idea there is an appropriate level of both mathematical … read more

The college algebra text covers all the typical topics for a course of this type. Within each idea there is an appropriate level of both mathematical rigor and application.

Though there were a few discrepancies between the online book and the hard copy and a couple of questionable solutions in the solutions manual, the accuracy of the text was excellent.

The text has up to date applications and connections. I see no reason why the types of questions and approaches the authors take will not make for a long lasting and relevant text.

The language and organization of the text is excellent. It is very readable and student friendly.

The text is very consistent in it’s approach to explanations and student engagement. Additionally, the notation used is clear and unambiguous, leading to strong student comprehension.

I did do a little reorganizing of the text. It seemed like some topics, like linear and quadratic equations, appeared and then disappeared, but reappeared later in a slightly new context. I thought it would have been better to keep them together so students could make more connections due to familiarity.

The text is very logically progressive and organized in such a way that both deductive and inductive methods of learning are present. It is consistently varied in that students are asked to think, explore and then do as a part of their learning engagement.

The text has clear visuals. The tables, charts, graphs and diagrams are easy to see and read.

The word choice of the text’s authors is excellent. Precise, but not so much jargon that the reader is consistently lost or needing to retrace their previous reading.

I didn’t notice any major flaws or positive aspects of the text, in this regard.

Thank you for putting such a fantastic resource together for students and professors. I will definitely use this again!

For a course titled College Algebra, all the topics covered and the level of rigor for those topics are mostly as one would expect. In addition, the … read more

For a course titled College Algebra, all the topics covered and the level of rigor for those topics are mostly as one would expect. In addition, the text contains chapters in Analytic Geometry as well as Sequences and Probability. The explanations are thorough yet not overly verbose. Throughout the text, the authors’ take the time to concisely explain the subject matter in natural language. Compared to the textbook currently in use by my institution, I would need to supplement a brief section on circles which serves as a reinforcement of the completing-the-square skill. Also, I would need additional linear application problems. (Problems dealing with motion, value/mixtures, simple interest, etc.) All relevant topics considered, there are only minor differences in content depth and breadth.

A spot check of a few problems per section from chapter 1 through 7 did not reveal any mistakes.

“I am Legend” is the top grossing horror movie of it’s decade? I’m sure I found that more interesting than people will 20 years from now. The content is timeless. The scenarios in which the content is applied are reasonably relevant. As far as I can predict, through the lens of now, the content will age well. In other words, no references to a fad were found. For example, word problems required no knowledge of Tamagotchi.

The clarity of this textbook was excellent. As mentioned before, the authors’ used clear and concise language throughout. As a litmus test, I like have a text-to-speech program narrate some passages. If the text-to-speech program doesn’t struggle, then I am more confident in the overall readability for a general audience. The text-to-speech program performed admirably. This is not a scientific process, but merely a way to inform my opinion. The presentation of concepts was logical and consistent with other textbooks that share the College Algebra title.

This textbook develops a method of presenting the material and sticks to that method throughout.

This textbook does a great job of breaking the content down into easily consumable chunks. It has a relatively high ratio of sections per number of pages. Each of those sections is broken up into: the standard hook example, brief content lecture, a couple example problems, a “try it” section for practice, additional explanation of the topic with a “Q&A” section, then further development of the section topic with more example problems. If I were to adopt this text, I would increase the number of bookmarks on the PDF so students could quickly get to the exercises at the end of each section.

Overall the organization of the text is logical and seems pedagogically justified. The layout is such that the transition from topic-to-topic from within a section and between sections is non-jarring and natural.

Visually they did a nice job of breaking up the content with the use of headings, varying fonts, font styles, and colors. The inclusion of video links at the end of each section is a nice value added feature. Again, personally, I would add more bookmarks to the PDF version. On a few occasions, I would have preferred the graphs right justified and the corresponding explanations left justified such that the size of the graph could have been increased. Similarly, there are a few points where I would have preferred the font to be a larger size. This is especially true in the exponential and logarithm sections. Since I can zoom, this is only a minor inconvenience. Structure-wise I would like to have more white space between paragraphs. I understand this a trade-off between readability vs. number of pages. If I’m using an electronic version, I’d prefer to error on the side of readability. For example, the four inequalities at the bottom of page 146 in the PDF version would have been more readable if stacked vertically than listed horizontally. These are minor issues. Overall the textbook has an attractive aesthetic and is nearly on par with modern retail offerings.

As far as I can tell the grammar is fine.

I did not discover any culturally insensitive or offensive material.

I appreciate all the time and effort the creators put into this project. It’s incredibly charitable and an impressive achievement in terms of quality. Any issue I mentioned was only to avoid writing the two word review, “It’s great.” I would have no reservations in adopting this textbook.

The text covers the full-set of expected material from a college algebra course with an emphasis on functions. There’s certainly more than a … read more

The text covers the full-set of expected material from a college algebra course with an emphasis on functions. There’s certainly more than a semester’s worth of material here and it would be fairly straightforward to pick and choose sections to tilt the text towards prefers topics. The table of contents contains easy and clear links to chapters and sections (even the PDF has links!). It could be improved with directions to each section’s glossary, key-ideas summary, and practice problems. Every section uses worked and explained examples to showcase ideas and has a full set of practice exercises.

I did not observe any mathematical errors, and the text’s error submission page appears impressively attended and well kept.

I encountered few examples that use time-sensitive data that would need to be updated frequently (teen texting habits from 2012 in 4.1 already feels dated). I do have concerns about the reliance on cell-phone per/minute plans that no longer represent the most common use-pattern and are unlikely to return to prominence. Algebra does not have to worry about obsolescence in quite the same way as other subjects, and there’s nothing to suggest the text will suddenly need major revisions.

Math textbooks are not easy reads for students, and I think most of mine would wish this had more examples with explained steps. Math jargon can be overwhelming and frequently the text and does extra work to clarify or define terms. Q&A’s right after new examples that illustrate potential problem areas preemptively but also in a more conversational tone. The online text has too many things in gray highlighting boxes, and lacks the visual contrast of the pdf. The online text’s graphs and visuals are great, but the tables really need better visual clarity. Overall I find the text more accessible than a standard math text.

The terminology seemed consistent throughout. Sections also follow similar patterns which make navigation and reading more straightforward.

Several of the sections contain too many topics and would be better served being separated into more manageable parcels. Being over-full of concepts can make it challenging for new students to identify patterns and then build the connections to old/new ideas as they just feel overwhelmed. Section 3.6 deserves special mention for being tightly focused to a specific idea (absolute value functions). There’s no way to make a math text fully modular but College Algebra does work to make topics self contained without repeating all prerequisites every time they’d appear.

The text is clearly organized and follows a logical progression. I found some of the sequencing unusual, but there’s clear reasoning and flow to the concept ordering.

I had no interface problems. However there are a variety of quality of life improvements that would make the text much more readable and approachable for students (not the same grey boxes everywhere please). Many things link in the online reader, but are missing specific labels. For instance, “Which table, Table, Table, or Table, representations a function (if any)? … A: Table and Table define functions…” I’m unclear why the online reader’s top ‘frame’ is eating as much screen space as it does. The search bar is a very nice feature and appears robust. The pdf’s graphs are too small by default, but can be zoomed in for clarity when needed. Chapter review exercises not being a separate section in the online reader (they’re tacked on to the end of the last section of a chapter) is a strange and disappointing choice. Many sections (it’s more common in the pdf) had links to 3-4 supplementary youtube videos before the practice exercises, which many of my students would appreciate. The end of section key-ideas summary contains links to specific worked examples which is wonderful.

I didn’t notice any egregious typos or grammatical mishaps.

There examples are by no means insensitive, but they are also not doing any particular work to be inclusive in the subject or topic representation. “Real-World Applications” examples vary wildly in quality, some are great and others undermine the “Real-World” label. References to sports and physics in introducing topics has the potential to be exclusionary for students without the needed backgrounds.

Overall College Algebra is a fine textbook, totally in line with common standards. For a potentially free-to-students option, that’s a tremendous achievement. Like many algebra textbooks there are issues with the presentation of mathematics as rote rules & procedures. Potentially attention grabbing introductory questions are left unanswered. Every section has a few extension questions, but there are few questions that would count as "Rich Mathematical Tasks" or demanding critical thinking. I do also wish a fully-digital text would provide a larger variety of fully-worked and explained solutions, and drop the convention of only providing answers to odd practice exercises. Too often ideas are introduced and explained via the fully-abstracted form, which only makes sense to readers already fluent in algebra. There are portions of the text that are vastly more approachable in their discussion of ideas and concepts than is common, and those, like the semi-frequent Q&A asides are where the text is at its best.

Any instructor teaching a college algebra class will find this text to be the perfect level of comprehensiveness. Some texts try to include too much … read more

Any instructor teaching a college algebra class will find this text to be the perfect level of comprehensiveness. Some texts try to include too much and some texts leave to much out. With this text you can tell that the authors strive and succeed at finding the perfect amount of information to present and discuss when teaching concepts. The text covers the standard college algebra topics in an order conducive to learning. They start essentially with basics and equations followed by functions and then on to (in standard order) the five main functions: Linear, Polynomial, Rational, Exponential and Logarithmic. Following these standard functions are thorough discussions for every optional subject that shows up in different schools under different instructors. These include: Systems of Equations, Conic Sections, Sequences, Counting and Probability. Each of these sections cover the material thoroughly and in a completely self-contained manner so as to allow the instructor flexibility of including or not including any of these sections without having to supplement.

A review of many of the examples in the sections and many of the homework problems and the solutions found at the end of the text have turned up no errors not already listed on the errata page. The authors have gone to great lengths to eliminate errors from the text. The authors have also decided to separate important definitions, results, concepts, and theorems in blue text boxes that direct the reader's attention as to say “something is really important here.” Extensive review of these important points are error-free concise and clear.

The content of college algebra has for the most part remained unchanged for years. This text is adequately relevant to the subject as it is taught today. There are very useful links to youtube videos that explain concepts. These links will have to be monitored for accuracy as the years go by in the event that the author of the videos moves and deletes videos. Furthermore, the use of real world examples in the chapter and the homework as informational/motivational pieces at the beginning of chapters are relevant and contain recent enough that students won't feel like they're reading a textbook from some other decade. I don't anticipate very many updates to the field of algebra, but if there are any, then the authors will be able to easily incorporate those updates in subsequent editions.

The book is written in a very clear concise manner that aims to teach in a self-contained manner. Student's will be able to pick up this book and learn from it with little outside supplementation. The jargon and technical terminology is perfect for a text at this level and teaches what needs to be taught. The authors walk students through learning in the way an instructor might do so in the classroom. The authors begin every section with clear expectations of learning objectives and then addresses each one of those objectives systematically including a “how to” section followed by examples showing students how to work problems followed by a “try it” section (with answers in the back of the book) allowing students to try their hand at problems. Often there are Q & A sections included that address the most common conceptual questions that instructors are asked by inquisitive students in the classroom. It is this organization/process that makes the book clear and easy to learn from.

This text is very consistent in the language used from section to section. The authors use terminology and symbols consistently from section to section and chapter to chapter. Besides consistency in the language used, the authors have managed to organize the chapters and sections with common fonts, text boxes, and overall layout so that students know what to expect and aren't distracted by the presentation while trying to learn new concepts

The chapters are appropriately designed and ordered. Each chapter is broken up nicely into sections. The text is sometimes self-referential, however, that is the nature of mathematics and scaffolding of learning is very much apart of that. The text could be easily reorganized if needed, but I think that the authors have really managed to organize the material in a way that is conducive to learning and I don't see why reorganization (except in perhaps very minor instances) would be needed. As mentioned before, the advanced chapters following logarithms are self-contained and can be taught in any order skipping chapters without loss of consistency.

The order of the topics presented progress from easier to more difficult in a logical manner starting with a strong foundation and building upon that foundation. Within each chapter, examples and explanations are logical and flow easily from easy to more difficult.

All navigation links to chapters and sections work well. The links to helpful youtube videos all work as well. The text uses appropriate organization of graphics and text highlighting important concepts in a non-distracting manner. Colors for text, fonts, headings are all appropriate and help to focus the reader's attention to what is truly important.

After reviewing this text for several weeks extensively, I have yet to find a grammatical error. The authors have worked very hard to eliminate errors from this text.

The text is not culturally insensitive or offensive in any way, however, there is really not too much effort to include examples or biographies that celebrate other cultures, ethnicities, or lifestyles. For example, using NFL examples are fine for the person that understands football, but this will not benefit students that have now knowledge of the NFL. If there is any room for improvement in this text this would be the area.

Here are some specific things that the book does really well. The examples in the homework do a great job of including problems that cater to the major areas of mathematics instruction namely: Graphical, analytical, numerical, and verbal. Calculator steps look like they cater to Texas Instruments. I'm not sure how this can be expanded to include other calculator manufacturers. Content-wise, the author does a great job of planting seeds early on for future learning. For example the authors introduce some simple transformations during the study of linear graphs before formally learning all of the other transformations in a later chapter. Later on, the authors do an exceptional job of teaching transformations including a very important and thorough discussion of how the order of transformations should be considered. This is something usually left out of most texts. The placement of even/odd functions immediately following reflections looks extremely effective! The authors seem to have found the perfect placement of this topic. There is an example or two of “solving logarithms mentally” which I believe goes a long way towards the goal of getting students to think about the mathematics they do. Discussion of conic sections are very thorough and even include derivations of the standard formulas! Here are a few things that I think the authors could consider for their next edition. The discussion of graphing non-linear inequalities hearkens back to a method used for graphing linear inequalities. However, the only graphing of linear inequalities I could find in the text is in one variable. There is no real coverage of graphing linear inequalities in two variables (in the xy-plane) which is really what is needed in order to move to the non-linear case analogously. Otherwise, the discussion of graphing non-linear inequalities is adequately thorough. Also, as a personal opinion, I don't think that partial fractions belong in a college algebra text. But if you are going to include such a section, then there should be some sort of discussion as to why you only need constant placeholders when dealing with linear factors in the denominator and why you need linear place holders when you have irreducible quadratics in the denominator. The method presented only gives “this is what you do” and no mention of why. Otherwise the placement right after systems of equations is a perfect application. Finally, in the matrices section the authors present the shortcut method for finding the determinant of a 3x3 matrix which is fine. The authors then point out that the method and not applicable to higher dimension matrices. The follow this with a statement that determinants of higher dimension matrices should be done with technology due to heavy computation. I would like to have seen a discussion of the general method of minor and co-factor expansions or at least a mention that there is a more general method that is “outside the scope of this text.” Other than these very minor improvements, this is a very well written text that any college algebra instructor could use with success. I plan on adopting this text for my classroom within the next year or so. Thanks to the authors for the hard work and a wonderful product!

The content of the text is quite comprehensive and certainly includes the relevant content that would be expected of a college algebra text. Some … read more

The content of the text is quite comprehensive and certainly includes the relevant content that would be expected of a college algebra text. Some might argue that trigonometric functions should be included in a college algebra text, yet I have found that most do not. The table of contents (in both the online and PDF versions) is very useful, considering it provides links that allow you to jump straight to a specific section. The section numbering system, however, is not consistent between the online and PDF versions, causing slight confusion (e.g. in the PDF version, "Quadratic Equations" is section 2.5, but in the online version it is section 2.6). This is because the online version assigns section 1 of each chapter to the introduction, whereas the PDF version assigns section 1 to the first section of actual content, thus causing the two versions to be one section "off" from each other. The index at the end of the book is also very useful, utilizing the links to quickly jump to specific pages where key terms are referenced.

The text appears to be very well done concerning accuracy. Furthermore, the author provides instructors with a quick and easy way to report any errors.

Typically, the main "content" of a college algebra text is not going to change over time, therefore the content in this text is up-to-date, relavent, and will not become obsolete any time soon. The authors do include multiple instances of modern examples within the technology and real-world applications sections of the exercises.

The text is pretty straight-forward with providing relevant content without excess dialogue or commentary.

The structure of the text is quite consistent. It is easy to navigate. From an instructor's point of view it should be easy to work through examples with students and provide ample opportunity to assign exercises.

The text provides a nice flow of commentary, figures, examples, etc.

The layout/order of the various sections within the text is definitely clear and logical.

As previously mentioned, there is a confusing inconsistency with section numbers between the online and PDF versions. Otherwise, the navigation is quite user-friendly. The links within the text that allow the user to jump to specific locations in the text (as opposed to excessive scrolling and manual searching) are quite useful.

The text appears to be grammatically sound.

I found no instances of culturally insensitive or offensive content.

The authors appear to have gone to great lengths to make this a user-friendly, comprehensive text. Furthermore, the inclusion of a wide variety of ancillary content for both instructors and students is much appreciated. I look forward to adopting this text for my college algebra sections.

## Table of Contents

## About the Book

*College Algebra* provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs. *College Algebra* guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they’ve learned.

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

## About the Contributors

### Author(s)

**Lead Author, Senior Content Expert**

Jay Abramson, Arizona State University

**Contributing Authors**

Valeree Falduto, Palm Beach State College

Rachael Gross, Towson University

David Lippman, Pierce College

Melonie Rasmussen, Pierce College

Rick Norwood, East Tennessee State University

Nicholas Belloit, Florida State College Jacksonville

Jean-Marie Magnier, Springfield Technical Community College

Harold Whipple, Formerly of Columbia College

Christina Fernandez