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.

Examples

Each learning objective is supported by one or more worked examples, that demonstrate the problem-solving approaches that students must master. The multiple Examples model different approaches to the same type of problem, or introduce similar problems of increasing complexity.

All Examples follow a simple two- or three-part format. The question clearly lays out a mathematical problem to solve. The Solution walks through the steps, usually providing context for the approach—in other words, why the instructor is solving the problem in a specific manner. Finally, the Analysis (for select Examples) reflects on the broader implications of the Solution just shown. Examples are followed by a Try It question, as explained below.

Figures

Algebra and Trigonometry contains 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 unobtrusive but important features contribute to and check understanding.

• 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 Web View version of the text, students can click an Answer link directly below the question to check their understanding. In the PDF, 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.

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 Algebra and Trigonometry.

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 6300 exercises across the 13 chapters, instructors should have plenty from which to choose¹.

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 to 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.

Additional Resources

Reviewers

Phil Clark, Scottsdale Community College

Michael Cohen, Hofstra University

Charles Conrad, Volunteer State Community College

David French, Tidewater Community College

Matthew Goodell, SUNY Ulster

Lance Hemlow, Raritan Valley Community College

Dongrin Kim, Arizona State University

Cynthia Landrigan, Eerie Community College

Wendy Lightheart, Lane Community College

Chinenye Ofodile, Albany State University

Carl Penziul, Tompkins-Cortland Community College

Sandra Nite, Texas A&M University

Eugenia Peterson, Richard J. Daley College

Rhonda Porter, Albany State University

Michael Price, University of Oregon

Steven Purtee, Valencia College

William Radulovich, Florida State College Jacksonville

Camelia Salajean, City Colleges of Chicago

Katy Shields, Oakland Community College

Nathan Schrenk, ECPI University

Pablo Suarez, Delaware State University

Allen Wolmer, Atlanta Jewish Academy

The following faculty contributed to the development of OpenStax Precalculus, the text from which this product was updated and derived.

Precalculus Reviewers

Nina Alketa, Cecil College

Kiran Bhutani, Catholic University of America

Brandie Biddy, Cecil College

Lisa Blank, Lyme Central School

Bryan Blount, Kentucky Wesleyan College

Jessica Bolz, The Bryn Mawr School

Sheri Boyd, Rollins College

Sarah Brewer, Alabama School of Math and Science

Charles Buckley, St. Gregory’s University
Michael Cohen, Hofstra University

Kenneth Crane, Texarkana College

Rachel Cywinski, Alamo Colleges

Nathan Czuba

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 Community College

Erinn Izzo, Nicaragua Christian Academy

John Jaffe

Jerry Jared, Blue Ridge School

Stan Kopec, Mount Wachusett Community College

Kathy Kovacs

Cynthia Landrigan, Erie Community College

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 at Austin

Rhonda Porter, Albany State University

Steven Purtee, Valencia College

William Radulovich, Florida State College Jacksonville

Alice Ramos, Bethel College

Nick Reynolds, Montgomery Community College

Amanda Ross, A. A. Ross Consulting and Research, LLC

Erica Rutter, Arizona State University

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 State University

John Thomas, College of Lake County

Diane Valade, Piedmont Virginia Community College

Allen Wolmer, Atlanta Jewish Academy