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Student Solutions Manual for Precalculus
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Description
- Updated Retain Your Knowledge problems in the exercise set improve student recall of concepts learned earlier in the course. These exercises are assignable in MyLab Math.
- Updated graphing images throughout each chapter show TI-84 Plus C and Desmos © screenshots. Using the graphing technology students are most familiar with, these images help students visualize concepts clearly and make stronger connections among equations, data and graphs in full color.
- Revised definitions — Definitions have been reviewed and, in a few cases, updated for consistency with those presented in Calculus. For example, in the definitions for increasing/decreasing functions, the word “open” has been deleted, allowing for functions to increase/decrease on any type of interval.
- The objective “Find the Equation of a Line Given Two Points” in Chapter F, Section 3 has been moved after the objective “Identify the Slope and y-Intercept of a Line from Its Equation.” This allows the authors to express lines in slope-intercept form.
Reach every student with MyLab
- Skill Builder offers adaptive practicethat is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
- Guided Visualizations help students better understand the visual aspects of key concepts in figure format. The figures are included in MyLab Math as both a teaching and an assignable learning tool.
- Updated Retain Your Knowledge Exercises support ongoing review at the course level and help students maintain essential skills. They are excellent cumulative review problems and ideal for studying for final exams. Available to assign in MyLab Math and in the text.
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Learning Catalytics™ helps you generate class discussion, guide your lecture, and promote peer-to-peer learning with real-time analytics.
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Now available through MyLab Math, Learning Catalytics is an interactive student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.
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Michael Sullivan III has written Learning Catalytics questions to engage students in your course.
Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before retiring recently. He is a native of Chicago’s South Side and divides his time between Oak Lawn, Illinois, and Naples, Florida.
Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows, and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America.
Mike has been writing textbooks for more than 35 years and currently has 15 books in print, 12 with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.
Mike has four children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his co-author on two precalculus series; Dan works in publishing; and Colleen teaches middle school and secondary school mathematics. Twelve grandchildren round out the family.
Mike Sullivan, III s a full-time professor at Joliet Jr. College with training in mathematics, statistics, and economics. Built from experience in the classroom using feedback from his students Mike has numerous Pearson textbooks in publication including a Developmental Math series and two Precalculus series and a statistics series. When not in the classroom or writing, you’ll find Mike trying to sneak in a round of golf if the schedules of his three children: Michael, Kevin, and Marissa allow it. Which might be a little easier now that Michael and Kevin are both in college.
Preparing for Class
- Just-in-time review begins all sections to prepare students for the topics ahead.
- Preparing for This Section lists previously learned concepts that will be useful in the section ahead. Page references are included for easy review.
- Now Work “Are You Prepared?” problems support the Preparing for This Section feature, allowing students to check that they are ready to proceed to the section ahead or if they need to turn back for further review. These problems appear at the start of each exercise set.
- Within each section, students get guidance along the way to help them master the material and develop their problem-solving skills.
- NEW! Desmos © screen captures have been added throughout the text, reflecting that graphing technology expands beyond graphing calculators.
- Now Work problems—many examples refer to a related problem in the exercise set, which are marked by a yellow pencil icon. If students get stuck while doing their homework, they can look for the closest Now Work problem and refer back to the related example.
- Step-by-Step, Annotated Examples contain detailed intermediate steps with additional annotations to help students see specific nuances.
Practicing Skills
- Updated – Retain Your Knowledge problems in the exercise set improve student recall of concepts learned earlier in the course. These exercises are assignable in MyLab Math.
- Assess Your Understanding appears at the end of every section and contains a variety of problems for students to master the skills they need.
- “Are You Prepared?” Problems appear at the start of every exercise set and help students determine exactly what they need to review and where to review it. This feature is referenced from the Preparing for This Section feature. Answers appear at the end of the section.
- Concepts and Vocabulary questions are fill-in the-blank and true/false items that assess students’ understanding of key definitions and concepts. These have been written to serve as reading quizzes and are now assignable in MyLab Math® and MathXL®.
- Skill Development problems provide straightforward practice, are organized by difficulty, and are correlated to section examples.
- Graphical problems use graphs in a variety of ways, supplementing students’ analytical understanding with graphical understanding.
- Mixed Practice problems offer comprehensive assessment of the skills learned in the section by asking questions that relate to more than one concept or objective. These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together.
- Applications and Extensions allow students to apply their skills to real-world problems and to extend concepts learned in the section.
- DWR—Discussion, Writing, and Research problems— are marked by a special icon and red numbers. They support class discussion, verbalization of mathematical ideas, and writing and research projects.
Reviewing Key Concepts for Exams and Quizzes
- Author in Action Videos are actual classroom lectures with fully worked out examples presented by Michael Sullivan III.
- Video assessment questions are available to assign in MyLab Math for key Author in Action videos.
- Updated- Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and book. By directing students into essential material, students can focus and retain the most important concepts. These notes help increase the success of your students in any course structure.
- Chapter Reviews at the end of each chapter offer a variety of convenient tools for students’ reference and review.
- Chapter Tests contain about 15-20 problems that can help students prepare for in-class exams. For additional help, students can watch an instructor work out full solutions on the Chapter Test Prep Video on YouTube™, or in MyLab Math.
- Cumulative Review problem sets appear at the end of every chapter after Chapter 1. They combine problems from previous chapters, providing an ongoing cumulative review.
Check out the preface for a complete list of features and what’s new in this edition.
Also available with MyLab Math
MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Learn more about MyLab Math.
Reach every student with MyLab
- Deliver trusted content: You deserve teaching materials that meet your own high standards for your course. That’s why we partner with highly respected authors to develop interactive content and course-specific resources that you can trust–and that keep your students engaged.
- Empower each learner: Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need — when and where they need it — to be successful.
- New – Skill Builder offers adaptive practicethat is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
- New – Guided Visualizations help students better understand the visual aspects of key concepts in figure format. The figures are included in MyLab Math as both a teaching and an assignable learning tool.
- Getting Ready material provides just-in-time review, integrated throughout the course as needed to prepare students with prerequisite material to succeed. From a quick quiz, a personalized, just-in-time review assignment is generated for each student, allowing them to refresh forgotten concepts.
- With Personalized Homework, students take a quiz or test and receive a subsequent homework assignment that is personalized based on their performance. This way, students can focus on just the topics they have not yet mastered.
- Teach your course your way: Your course is unique. So whether you’d like to build your own assignments, teach multiple sections, or set prerequisites, MyLab gives you the flexibility to easily create your course to fit your needs.
- Enhanced Sample Assignments by Michael Sullivan III make course set-up easier by giving instructors a starting point for each section. Each assignment, handpicked by the author to align with this text, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic.
- Learning Catalytics™ helps you generate class discussion, guide your lecture, and promote peer-to-peer learning with real-time analytics.
- Now available through MyLab Math, Learning Catalytics is an interactive student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.
- Michael Sullivan III has written Learning Catalytics questions to engage students in your course.
- Improve student results: When you teach with MyLab, student performance improves. That’s why instructors have chosen MyLab for over 20 years, touching the lives of over 50 million students.
F. Foundations: A Prelude to Functions
F.1 The Distance and Midpoint Formulas
F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
F.3 Lines
F.4 Circles
1. Functions and Their Graphs
1.1 Functions
1.2 The Graph of a Function
1.3 Properties of Functions
1.4 Library of Functions; Piecewise-defined Functions
1.5 Graphing Techniques: Transformations
1.6 Mathematical Models: Constructing Functions
1.7 Building Mathematical Models Using Variation
Chapter Review
Chapter Test
Chapter Projects
2. Linear and Quadratic Functions
2.1 Properties of Linear Functions and Linear Models
2.2 Building Linear Models from Data
2.3 Quadratic Functions and Their Zeros
2.4 Properties of Quadratic Functions
2.5 Inequalities Involving Quadratic Functions
2.6 Building Quadratic Models from Verbal Descriptions and from Data
2.7 Complex Zeros of a Quadratic Function
2.8 Equations and Inequalities Involving the Absolute Value Function
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
3. Polynomial and Rational Functions
3.1 Polynomial Functions and Models
3.2 The Real Zeros of a Polynomial Function
3.3 Complex Zeros; Fundamental Theorem of Algebra
3.4 Properties of Rational Functions
3.5 The Graph of a Rational Function
3.6 Polynomial and Rational Inequalities
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
4. Exponential and Logarithmic Functions
4.1 Composite Functions
4.2 One-to-One Functions; Inverse Functions
4.3 Exponential Functions
4.4 Logarithmic Functions
4.5 Properties of Logarithms
4.6 Logarithmic and Exponential Equations
4.7 Compound Interest
4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay
4.9 Building Exponential, Logarithmic, and Logistic Functions from Data
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
5. Trigonometric Functions
5.1 Angles and Their Measure
5.2 Right Triangle Trigonometry
5.3 Computing the Values of Trigonometric Functions of Acute Angles
5.4 Trigonometric Functions of Any Angle
5.5 Unit Circle Approach; Properties of the Trigonometric Functions
5.6 Graphs of the Sine and Cosine Functions
5.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
5.8 Phase Shift; Sinusoidal Curve Fitting
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
6. Analytic Trigonometry
6.1 The Inverse Sine, Cosine, and Tangent Functions
6.2 The Inverse Trigonometric Functions (Continued)
6.3 Trigonometric Equations
6.4 Trigonometric Identities
6.5 Sum and Difference Formulas
6.6 Double-angle and Half-angle Formulas
6.7 Product-to-Sum and Sum-to-Product Formulas
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
7. Applications of Trigonometric Functions
7.1 Right Triangle Trigonometry; Applications Involving Right Triangles
7.2 The Law of Sines
7.3 The Law of Cosines
7.4 Area of a Triangle
7.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
8. Polar Coordinates; Vectors
8.1 Polar Coordinates
8.2 Polar Equations and Graphs
8.3 The Complex Plane; DeMoivre’s Theorem
8.4 Vectors
8.5 The Dot Product
8.6 Vectors in Space
8.7 The Cross Product
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
9. Analytic Geometry
9.1 Conics
9.2 The Parabola
9.3 The Ellipse
9.4 The Hyperbola
9.5 Rotation of Axes; General Form of a Conic
9.6 Polar Equations of Conics
9.7 Plane Curves and Parametric Equations
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
10. Systems of Equations and Inequalities
10.1 Systems of Linear Equations: Substitution and Elimination
10.2 Systems of Linear Equations: Matrices
10.3 Systems of Linear Equations: Determinants
10.4 Matrix Algebra
10.5 Partial Fraction Decomposition
10.6 Systems of Nonlinear Equations
10.7 Systems of Inequalities
10.8 Linear Programming
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
11. Sequences; Induction; the Binomial Theorem
11.1 Sequences
11.2 Arithmetic Sequences
11.3 Geometric Sequences; Geometric Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
12. Counting and Probability
12.1 Counting
12.2 Permutations and Combinations
12.3 Probability
Chapter Review
Chapter Test
Chapter Projects
Cumulative Review
13. A Preview of Calculus: The Limit, Derivative, and Integral of a Function
13.1 Finding Limits Using Tables and Graphs
13.2 Algebra Techniques for Finding Limits
13.3 One-sided Limits; Continuous Functions
13.4 The Tangent Problem; The Derivative
13.5 The Area Problem; The Integral
Chapter Review
Chapter Test
Chapter Projects
Appendix A. Review
A.1 Algebra Essentials
A.2 Geometry Essentials
A.3 Polynomials
A.4 Factoring Polynomials
A.5 Synthetic Division
A.6 Rational Expressions
A.7 nth Roots; Rational Exponents
A.8 Solving Equations
A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs
A.10 Interval Notation; Solving Inequalities
A.11 Complex Numbers
Appendix B. Graphing Utilities
B.1 The Viewing Rectangle
B.2 Using a Graphing Utility to Graph Equations
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
B.4 Using a Graphing Utility to Solve Equations
B.5 Square Screens
B.6 Using a Graphing Utility to Graph Inequalities
B.7 Using a Graphing Utility to Solve Systems of Linear Equations
B.8 Using a Graphing Utility to Graph a Polar Equation
B.9 Using a Graphing Utility to Graph Parametric Equations
Answers
Index
Additional information
| Dimensions | 2.00 × 8.60 × 10.80 in |
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| Subjects | mathematics, higher education, Precalculus |