xxii Preface to the Instructor • In Words notes are used to help students focus on a concept or a formula, definition, or theorem being presented. • A Note is used at times to further clarify reasoning or make connections to prior concepts. • Seeing the Concept margin notes are strategically provided where graphing exploration may be useful to strengthen understanding of a mathematical concept. • Career Tips and Fun Facts are provided occasionally to help students connect the topic being discussed to the world around them. • Caution margin notes are used to help students avoid common mistakes that we all make when first learning a new mathematical skill. • Retain Your Knowledge Problems These problems are based on the article “To Retain New Learning, Do the Math,” published in the Edurati Review. In this article, Kevin Washburn suggests that “the more students are required to recall new content or skills, the better their memory will be.” In most sections, problems were chosen that preview skills required to succeed in subsequent sections. All answers to Retain Your Knowledge problems are given in the back of the text and all are assignable in MyMathLab for School. • NEW! Video Note-Taking Guide Ideal for online, emporium/redesign courses, flipped classrooms, or traditional lecture classrooms. The note-taking guide helps students take thorough, organized, and understandable notes as they watch the new instructional videos. They ask students to complete definitions, procedures, and examples based on the content of the videos and text. In addition, experience suggests that students learn by doing and understanding the why/how of the concept or property. Therefore, many sections will have an expoloration activity to motivate student learning. These explorations introduce the topic and/or connect it to either a real-world application or a previous section. For example, when the vertical-line test is discussed in Section 2.2, after the theorem statement, the notes ask the students to explain why the vertical-line test works by using the definitions of a function. This challenge helps students process the information at a higher level of understanding. • Chapter Projects apply the concepts of each chapter to a real-world situation that is current and relevant today. Many of these projects embrace the spirit of active learning by requiring the student to research information online in order to solve problems. • Exercise Sets The exercises in the text have been reviewed and analyzed. Some have been removed and new ones have been added. All time-sensitive problems, espcially those involving data, have been updated to the most recent information available. The problem sets remain classified according to purpose. The ‘Are You Prepared?’ problems serve their purpose as a just-in-time review of concepts that the student will need to apply in the upcoming section. The Concepts and Vocabulary problems cover each objective of the section. These multiple-choice, fill-in-the-blank, and True/False exercises have been written to also serve as reading quizzes. Skill Building problems develop the student’s computational skills with a large selection of exercises that are directly related to the objectives of the section. Often the Skill Building problems begin with Interactive Figure Exercises. Mixed Practice problems offer a comprehensive assessment of skills that relate to more than one objective. Often these require skills learned earlier in the course which helps students retain their knowledge. Applications and Extensions problems have been updated. Further, many new application-type exercises have been added, especially ones involving information and data drawn from sources the student will recognize, to improve relevance and timeliness. At the end of Applications and Extensions, we have a collection of one or more Challenge Problems . These problems, as the title suggests, are intended to be thought-provoking, requiring some ingenuity to solve. They can be used for group work or to challenge students. At the end of the Annotated Instructor’s Edition and in the online Instructor’s Solutions Manual, we have provided solutions to all these problems. The Explaining Concepts exercises provide opportunity for classroom discussion and group projects. • Diversity, Equity, and Inclusion— Pearson conducted an external review of the text’s content to determine how it could be improved to address issues related to diversity, equity, and inclusion.The results of that review informed this revision. • Key to Exercise Types— To help you navigate the features of the exercise sets, we’ve included a key at the bottom of the first page of each section’s exercises. 1. Now Work 1. Modeling 1. Explaining Concepts Calculus Preview 1. Interactive Figure Content Changes to the 9 th edition Chapter 1 • Exercises have been updated with current and relevant scenarios such as credit card debt and revenue earned by social media influencers. • NEW Desmos and GeoGebra screenshots added to illustrate how to graph equations, create tables, and solve equations. Chapter 2 • NEW Desmos and GeoGebra screenshots added to illustrate the use of function notation and finding points of interest such as local extrema. • Continued updates to exercises with current data and relevance.
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