Precalculus

Learning Objectives

Each chapter is divided into multiple sections (or modules), each of which is organized around a set of learning objectives. The learning objectives are listed explicitly at the beginning of each section, and are the focal point of every instructional element

Narrative text

Narrative text is used to introduce key concepts, terms, and definitions, to provide real-world context, and to provide transitions between topics and examples. Throughout this book, we rely on a few basic conventions to highlight the most important ideas:

• Key terms are boldfaced, typically when first introduced and/or when formally defined
• Key concepts and definitions are called out in a blue box for easy reference.
• Key equations, formulas, theorems, identities, etc. are assigned a number, which appears near the right margin. Occasionally the text may refer back to an equation or formula by its number.

Example

Each learning objective is supported by one or more worked examples, which demonstrate the problem-solving approaches that students must master. Typically, we include multiple Examples for each learning objective in order to model different approaches to the same type of problem, or to introduce similar problems of increasing complexity. All told, there are more than 650 Examples, or an average of about 55 per chapter.

All Examples follow a simple two- or three-part format. First, we pose a problem or question. Next, we demonstrate the Solution, spelling out the steps along the way. Finally (for select Examples), we conclude with an Analysis reflecting on the broader implications of the Solution just shown.

Figures

Openstax contains more than 2000 figures and illustrations, the vast majority of which are graphs and diagrams. Art throughout the text adheres to a clear, understated style, drawing the eye to the most important information in each figure while minimizing visual distractions. Color contrast is employed with discretion to distinguish between the different functions or features of a graph.

Supporting Features

Four small but important features, each marked by a distinctive icon, serve to support Examples.

A “How To” is a list of steps necessary to solve a certain type of problem. A How To typically precedes an Example that proceeds to demonstrate the steps in action.

A “Try It” exercise immediately follows an Example or a set of related Examples, providing the student with an immediate opportunity to solve a similar problem. In the Online version of the text, students can click an Answer link directly below the question to check their understanding. In other versions, answers to the Try-It exercises are located in the Answer Key.

A Q&A may appear at any point in the narrative, but most often follows an Example. This feature pre-empts misconceptions by posing a commonly asked yes/no question, followed by a detailed answer and explanation.

The “Media” icon appears at the conclusion of each section, just prior to the Section Exercises. This icon marks a list of links to online video tutorials that reinforce the concepts and skills introduced in the section.

Disclaimer: While we have selected tutorials that closely align to our learning objectives, we did not produce these tutorials, nor were they specifically produced or tailored to accompany Openstax . We are deeply grateful to James Sousa for compiling his incredibly robust and excellent library of video tutorials, which he has made available to the public under a CC-BY-SA license at http://mathispower4u.yolasite.com/. Most or all of the videos to which we link in our “Media” feature (plus many more) are found in the Algebra 2 and Trigonometry video libraries at the above site.

Section Exercises

Each section of every chapter concludes with a well-rounded set of exercises that can be assigned as homework or used selectively for guided practice. With over 5900 exercises across the 12 chapters, instructors should have plenty to choose from

Section Exercises are organized by question type, and generally appear in the following order:

• Verbal questions assess conceptual understanding of key terms and concepts.
• Algebraic problems require students to apply algebraic manipulations demonstrated in the section.
• Graphical problems assess students’ ability to interpret or produce a graph.
• Numeric problems require the student perform calculations or computations.
• Technology problems encourage exploration through use of a graphing utility, either to visualize or verify algebraic results or to solve problems via an alternative to the methods demonstrated in the section.
• Extensions pose problems more challenging than the Examples demonstrated in the section. They require students to synthesize multiple learning objectives or apply critical thinking to solve complex problems.
• Real-World Applications present realistic problem scenarios from fields such as physics, geology, biology, finance, and the social sciences.

Chapter Review Features

Each chapter concludes with a review of the most important takeaways, as well as additional practice problems that students can use to prepare for exams.

• Key Terms provides a formal definition for each bold-faced term in the chapter.
• Key Equations presents a compilation of formulas, theorems, and standard-form equations.
• Key Concepts summarizes the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.
• Chapter Review Exercises include 40-80 practice problems that recall the most important concepts from each section.
• Practice Test includes 25-50 problems assessing the most important learning objectives from the chapter. Note that the practice test is not organized by section, and may be more heavily weighted toward cumulative objectives as opposed to the foundational objectives covered in the opening sections.
• Answer Key includes the answers to all Try It exercises and every other exercise from the Section Exercises, Chapter Review Exercises, and Practice Test.

Ancillaries

OpenStax projects offer an array of ancillaries for students and instructors. Currently the following resources are available.

• Instructor’s Solutions Manual
• Student’s Solutions Manual
• PowerPoint Slides

Please visit http://openstaxcollege.org to view an up-to-date list of the Learning Resources for this title and to find information on accessing these resources.

Online Homework

WebAssign is an independent online homework and assessment solution first launched at North Carolina State University in 1997. Today, WebAssign is an employee-owned benefit corporation and participates in the education of over a million students each year. WebAssign empowers faculty to deliver fully customizable assignments and high quality content to their students in an interactive online environment. WebAssign supports with hundreds of problems covering every concept in the course, each containing algorithmically-generated values and links directly to the eBook providing a completely integrated online learning experience.

Learningpod is the best place to find high-quality practice and homework questions. Through our partnership with OpenStax College we offer easy-to-use assignment and reporting tools for professors and a beautiful practice experience for students. You can find questions directly from this textbook on Learningpod.com or through the OpenStax mobile app. Look for our links at the end of each chapter!
Practice questions on the Learningpod website: www.learningpod.com
Download the OpenStax Companion Workbooks app (iOS): http://bit.ly/openstaxworkbooks

Lead Author, Senior Content Expert

Jay Abramson has been teaching for 33 years, the last 14 at Arizona State University, where he is a principal lecturer in the School of Mathematics and Statistics. His accomplishments at ASU include co-developing the university’s first hybrid and online math courses as well as an extensive library of video lectures and tutorials. In addition, he has served as a contributing author for two of Pearson Education’s math programs, NovaNet and Trigonometry. Prior to coming to ASU, Jay taught at Texas Tech University and Amarillo College. He received Teacher of the Year awards at both institutions.

Contributing Authors

• Valeree Falduto, Palm Beach State College
• Rachael Gross, Towson State 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
• Christina Fernandez

Faculty Reviewers and Consultants

• Nina Alketa, Cecil College
• Kiran Bhutani, Catholic University
• Brandi Biddy, Cecil College
• Lisa Blank, Lyme Central School
• Bryan Blount, Kentucky Wesleyan College
• Charles Buckley, St. Gregory's University
• Michael Cohen, Hofstra University
• Kenneth Crane, Texarkana College
• Srabasti Dutta, Ashford University
• Kristy Erickson, Cecil College
• Nicole Fernandez, Georgetown University / Kent State University
• David French, Tidewater Community College
• Douglas Furman, SUNY Ulster
• Lance Hemlow, Raritan Valley CC
• Stan Kopec, Mount Machusett Community College
• Jerry Jared, The Blue Ridge School
• Sara Lenhart, Christopher Newport University
• Wendy Lightheart, Lane Community College
• Joanne Manville, Bunker Hill Community College
• Karla McCavit, Albion College
• Cynthia McGinnis, Northwest Florida State College
• Lana Neal, University of Texas
• Rhonda Porter, Albany State University
• Steven Purtee, Valencia College
• William Radulovich, Florida State College Jacksonville
• Alice Ramos, Bethel College
• Nick Reynolds, Montgomery Community College
• Sutandra Sarkar, Georgia State University
• Willy Schild, Wentworth Institute of Technology
• Todd Stephen, Cleveland State University
• Scott Sykes, University of West Georgia
• Linda Tansil, Southeast Missouri University
• John Thomas, College of Lake County
• Diane Valade, Piedmont Virginia Community College