Algebra and Trigonometry

Description

 

About the Book

• Functions appear early and are integrated, reflecting the authors’ belief that functions are best taught as a theme of the course, not as an isolated topic.
• Functions are introduced in Chapter 1, so that students to start the course with a new topic rather than a review of equation-solving that was covered in previous math courses.
• Students will come to understand the concept of a function by being exposed repeatedly to the language, notation, and use of functions throughout the text.
• The authors take a visual approach to the course. The early introduction to functions allows for the use of graphs to provide a visual aspect to solving equations and inequalities. In addition, specific features enable students to “see the math” and make connections between concepts.
• Algebraic/Graphical Side-by-Side Examples present the solutions in a two-column format to help students understand the connection between algebraic manipulation and the graphical interpretation.
• Visualizing the Graph exercises help develop students’ ability to make the mental link between different types of equations and their corresponding graphs.
• Connecting the Concepts, a hallmark feature of the text, invites the student to stop and check their understanding of how concepts work together in one section or several sections. Concepts are summarized visually—using graphs, outlines, or charts—so that students deepen their understanding and make connections.

• Ongoing review features throughout the text reinforce the concepts and help students build understanding.
• NEW! Just-In-Time Review: Review of prerequisite algebra topics is now presented when students need it most.
• A set of 25 numbered short review topics creates an efficient review of intermediate algebra topics.
• This feature is placed at the back of the text. Just-In-Time icons are positioned throughout the text next to the example where review of an intermediate algebra topic would be helpful.
• The Just-In-Time review topics are assignable in MyMathLab.
• Even more just-in-time review resources are available in the MyMathLab course for College Algebra with Integrated Review and in the Getting Ready MyMathLab exercises.

• Mid-chapter Review exercises are one-page mixed review sets at logical breaks in the chapter, helping students to reinforce their understanding of the concepts. These exercises are assignable in MyMathLab.
• Vocabulary Review exercises appear in the last section of each chapter, and check students’ understanding of the language of mathematics. These are now assignable in MyMathLab and can serve as reading quizzes.
• Synthesis exercises, included at the end of each exercise set, encourage critical thinking by asking students to apply multiple skills or concepts within a single exercise. For the Fourth Edition, these are assignable in MyMathLab.
• Classify the Function exercises, appearing in the Skill Maintenance section of the exercise sets, ask students to identify a number of functions by their type (linear, quadratic, rational, etc.). Throughout the text, the variety of functions increases and these exercises become more challenging.
• Review Icons refer students to an earlier, related section where they can go to review prerequisite concepts that are needed for the current section.
• Technology Connections are optional sections that guide students in the use of the graphing calculator as another way to check problems.

Zeros, Solutions, and x-Intercepts are a theme of the text. The authors aim to help students see the connection between the real zeros of the function, the solutions of the associated equation, and the first coordinates of the x-intercepts of the graph. When students develop their understanding of these connections, their probability of success increases for this course.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

 

With this edition, the authors focused on MyMathLab features that help better prepare students and get them thinking more visually and conceptually.

• MyMathLab is closely integrated with the text and offers a variety of question types, for a robust online experience that mirrors the authors’ approach.

• MyMathLab with Integrated Review is a new course option that includes additional review resources (skill check quizzes, personalized homework, review worksheets, and videos) at the beginning of each chapter in the College Algebra course.
• NEW! 25 Just-In-Time review topics are assignable in MyMathLab.
• NEW! Video Assessment is tied to the Example-based videos, created by the authors, which walk students through the detailed solution process for key examples in the textbook. Videos have optional subtitles. Instructors can assign these videos and check for students’ conceptual understanding.
• NEW! Video Notebook contains fill-in-the-blank worksheets to accompany the video examples presented by the authors. Key definitions, theorems, and procedures are also included. After filling in the worksheet while watching the video, the student has an excellent study guide for review and test preparation. This is available in print or as a PDF or Word document in MyMathLab.

• NEW! Getting Ready: skill review quizzes are assignable throughout the course, testing students on prerequisite knowledge. From these quizzes, each student receives a personalized homework assignment to refresh forgotten concepts.
• NEW! Adaptive Study Plan: MyMathLab now offers adaptive learning functionality that continuously analyzes student work and points them toward resources that will maximize their potential for understanding and success.
• NEW! Skills for Success Module: these modules help students develop the good habits needed in the transition to college and then to professional life.
• NEW! Enhanced Graphing Functionality: New functionality within the graphing utility allows graphing of 3-point quadratic functions, 4-point cubic graphs, and transformations in exercises.
• Vocabulary exercises serve as reading quizzes and help ensure that students have a good grasp of the necessary terminology.
• Mid-chapter Reviews are assignable, helping students to reinforce their understanding of the concepts.
• Synthesis exercises are assignable, testing students’ ability to answer questions that cover multiple concepts.
• Sample homework assignments are pre-selected by the authors for each section. These are indicated in the Annotated Instructor Edition by a blue underline within each end-of-section exercise set. These homework sets are assignable in MyMathLab.

1. Graphs, Functions, and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities
2. More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
2.3 The Composition of Functions
2.4 Symmetry
2.5 Transformations
2.6 Variation and Applications
3. Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
3.4 Solving Rational Equations and Radical Equations
3.5 Solving Equations and Inequalities with Absolute Value
4. Polynomial Functions and Rational Functions
4.1 Polynomial Functions and Models
4.2 Graphing Polynomial Functions
4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions
4.6 Polynomial Inequalities and Rational Inequalities
5. Exponential Functions and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest
6. The Trigonometric Functions
6.1 Trigonometric Functions of Acute Angles
6.2 Applications of Right Triangles
6.3 Trigonometric Functions of Any Angle
6.4 Radians, Arc Length, and Angular Speed
6.5 Circular Functions: Graphs and Properties
6.6 Graphs of Transformed Sine and Cosine Functions
7. Trigonometric Identities, Inverse Functions, and Equations
7.1 Identities: Pythagorean and Sum and Difference
7.2 Identities: Cofunction, Double-Angle, and Half-Angle
7.3 Proving Trigonometric Identities
7.4 Inverses of the Trigonometric Functions
7.5 Solving Trigonometric Equations
8. Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Complex Numbers: Trigonometric Notation
8.4 Polar Coordinates and Graphs
8.5 Vectors and Applications
8.6 Vector Operations
9. Systems of Equations and Matrices
9.1 Systems of Equations in Two Variables
9.2 Systems of Equations in Three Variables
9.3 Matrices and Systems of Equations
9.4 Matrix Operations
9.5 Inverses of Matrices
9.6 Determinants and Cramer’s Rule
9.7 Systems of Inequalities and Linear Programming
9.8 Partial Fractions
10. Conic Sections
10.1 The Parabola
10.2 The Circle and the Ellipse
10.3 The Hyperbola
10.4 Nonlinear Systems of Equations and Inequalities
10.5 Rotation of Axes
10.6 Polar Equations of Conics
10.7 Parametric Equations
11. Sequences, Series, and Combinatorics
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
11.4 Mathematical Induction
11.5 Combinatorics: Permutations
11.6 Combinatorics: Combinations
11.7 The Binomial Theorem
11.8 Probability

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University—Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren, and promoting charity projects for a children’s camp.

Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University—Purdue University Indianapolis (IUPUI) and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit and spend time with her children.

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University—Purdue University Indianapolis (IUPUI), and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled “Baseball and Mathematics.” In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

For courses in algebra and trigonometry.

Visualize. Interact. Succeed.

Beecher, Penna, and Bittinger’s Algebra and Trigonometry is known for enabling students to “see the math” through its focus on visualization and early introduction to functions. With the Fifth Edition, the authors continue to innovate by creating and positioning review material to provide a more effective tool for teachers and students.

25 Just-In-Time review topics are placed throughout the text and MyMathLab to help students right when they need it most. This, along with the existing Mid-chapter Mixed Review exercises, Study Guide summaries, and the new MyMathLab with Integrated Review course, students have an unparalleled amount of review resources to help them be successful in the course.

Also available with MyMathLab^®

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, the authors focused on developing MyMathLab features that help better prepare students and get them thinking more visually and conceptually.

For courses in algebra and trigonometry.

 

Visualize. Interact. Succeed.

Beecher, Penna, and Bittinger’s Algebra and Trigonometry is known for enabling students to “see the math” through its focus on visualization and early introduction to functions. With the Fifth Edition, the authors continue to innovate by creating and positioning review material to provide a more effective tool for teachers and students.

 

25 Just-In-Time review topics are placed throughout the text and MyMathLab to help students right when they need it most. This, along with the existing Mid-chapter Mixed Review exercises, Study Guide summaries, and the new MyMathLab with Integrated Review course, students have an unparalleled amount of review resources to help them be successful in the course.

 

Also available with MyMathLab^®

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, the authors focused on developing MyMathLab features that help better prepare students and get them thinking more visually and conceptually.

 

 

 

 

New and updated features

• Just-In-Time Review: Review of prerequisite algebra topics is now presented when students need it most.
• A set of 25 numbered short review topics creates an efficient review of intermediate algebra topics.
• This feature is placed at the back of the text. Just-In-Time icons are positioned throughout the text next to the example where review of an intermediate algebra topic would be helpful.
• The Just-In-Time review topics are assignable in MyMathLab.
• Even more just-in-time review resources are available in the MyMathLab course for College Algebra with Integrated Review and in the Getting Ready MyMathLab exercises.
• Data-Informed Exercises: Through analyzing MyMathLab usage data, the authors have revised exercises for this new edition. The goal is to ultimately improve the quality and quantity of exercises that matter the most to instructors and students For example, the authors adjusted sample homework assignments to ensure usage of the most widely-used exercises.
• Symmetry and Transformations: These topics are now presented in two sections rather than one due to reviewer feedback. Separating these concepts into two reasonable amounts of information allows for deeper student understanding.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, the authors focused on MyMathLab features that help better prepare students and get them thinking more visually and conceptually.

• 25 Just-In-Time review topics are assignable in MyMathLab.
• Video Assessment is tied to the Example-based videos, created by the authors, which walk students through the detailed solution process for key examples in the textbook. Videos have optional subtitles. Instructors can assign these videos and check for students’ conceptual understanding.
• Video Notebook contains fill-in-the-blank worksheets to accompany the video examples presented by the authors. Key definitions, theorems, and procedures are also included. After filling in the worksheet while watching the video, the student has an excellent study guide for review and test preparation. This is available in print or as a PDF or Word document in MyMathLab.
• Getting Ready: skill review quizzes are assignable throughout the course, testing students on prerequisite knowledge. From these quizzes, each student receives a personalized homework assignment to refresh forgotten concepts.
• Adaptive Study Plan: MyMathLab now offers adaptive learning functionality that continuously analyzes student work and points them toward resources that will maximize their potential for understanding and success.
• Skills for Success Module: these modules help students develop the good habits needed in the transition to college and then to professional life.
• Enhanced Graphing Functionality: New functionality within the graphing utility allows graphing of 3-point quadratic functions, 4-point cubic graphs, and transformations in exercises.

 

Additional information

Dimensions	1.80 × 8.50 × 10.80 in
Imprint	Pearson
Format	gen
ISBN-13	09780321969569
ISBN-10	0321969561
Author	Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Subjects	mathematics, higher education, Precalculus, Algebra and Trigonometry