Student Solutions Manual for Algebra and Trigonometry Enhanced with Graphing Utilities

Description

• Need to Review? reminders now appear in the margin for key review topics, pointing students to the location of the review material in the textbook.
• Graphing Utility Screen Captures — Desmos screen captures have been added in several instances, along with the TI-84 Plus CE screen captures. These updated screen captures provide alternative ways of visualizing concepts and making connections between equations, data, and graphs in full color.
• New and enhanced Chapter Projects give students an up-to-the-minute experience. Many of the new projects require students  to research information online in order to solve problems.
• Interactive Figure Exercises is a new category of exercises requiring students to manipulate an interactive figure to solve. Created by author Michael Sullivan III in GeoGebra, the interactive figures may be found at bit.ly/2MibgaO or in the Video and Resource Library of MyLab Math. These exercises are labeled with a special icon.
• Expanded Retain Your Knowledge problems:
• While the focus of these problems remains the maintenance of students’ skills, in most sections problems preview skills students need to succeed in subsequent sections or in calculus. These are easily identified by a calculus icon. 
• All answers to Retain Your Knowledge problems are given in the back of the text and these problems are included in pre-built Enhanced Sample Assignments.
• Challenge Problems now appear in the Applications and Extensions part of the section exercises, for students seeking problems with greater rigor. 
• Key to Exercise Types helps users navigate the features of the exercise sets with a key at the bottom of the first page of each section’s exercises.

Check out the preface for a complete list of features and what’s new in this edition.

Also available with MyLab Math 

• Enhanced Sample Assignments are pre-made section-level assignments that address key concepts within the section and help keep previously learned skills fresh with Retain Your Knowledge question. They are assignable and editable.
• Setup & Solve Exercises require students to show how they set up a problem as well as the solution, better mirroring what is required of them on tests. We have included both the “traditional” and Setup & Solve versions of exercise within MyLab to provide you with more options for assessing students.
• Integrated Review content and assessments help you provide students with just the remediation they need, when they need it. Integrated Review consists of:
• Skills Check Quizzes by chapter assess the prerequisite skills students need for that chapter.
• Personalized Skills Review Homework is generated for each student based on the results of the Skills Check Quiz to provide students with help on the prerequisite skills they are lacking. Students receive just the help they need–no more, no less.
• Algebra Review eText, Exercises, Videos, and Worksheets are offered for students who need more help (or for co-requisite courses). There’s no need to go elsewhere for remediation.
• Interactive Figures (formerly titled Guided Visualizations) — The suite of Interactive Figures has been expanded to support teaching and learning. The figures (created in GeoGebra by author Michael Sullivan III) illustrate key concepts and allow manipulation. They have been designed to be used in lectures as well as by students independently.

• Personal Inventory Assessments are a collection of online exercises designed to promote self-reflection and engagement in students. These 33 assessments include topics such as a Stress Management Assessment, Diagnosing Poor Performance and Enhancing Motivation, and Time Management Assessment. 

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.
• 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.
• Section-level guidance helps students master the material and develop their problem-solving skills:
• NEW – Need to Review? reminders now appear in the margin for key review topics, pointing students to the location of the review material in the textbook.
• Showcase Examples provide how-to instruction by offering a guided, step-by-step approach to solving a problem. Students can immediately see how each of the steps in a problem is employed. 
• Model It examples are now highlighted, making it easy to identify which examples help students learn to build a mathematical model from verbal descriptions or from data. Model It exercises are included to assign for homework or practice.
• Now Work problems follow most examples and point to a related exercise for immediate reinforcement of the skill or concept.
• Calculus icons appear next to information essential for the study of calculus. When the icon appears next to a definition, the notation used is consistent with that used in calculus.

 

Practicing skills

• UPDATED – Guided Lecture Notes ask students to complete definitions, procedures, and examples based on the content of the Author in Action videos and text. 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.
• NEW – Graphing Utility Screen Captures – Desmos™ screen captures have been added in several instances along with the TI-84 Plus CE screen captures. These updated screen captures provide alternative ways of visualizing concepts and making connections between equations, data, and graphs in full color.
• NEW / REVISED – Chapter Projects give students an up-to-the-minute experience. Many of the new projects require students  to research information online in order to solve problems.

• Assess Your Understanding appears at the end of every section and contains a variety of problems for students to master the skills they need.
• 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.
• 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. These exercises have been updated and many new problems have been added.
• NEW – Challenge Problems now appear in the Applications and Extensions part of the section exercises, for students seeking problems with greater rigor. 
• NEW – Interactive Figure Exercises is a new category of exercises requiring students to manipulate an interactive figure to solve. Created by author Michael Sullivan III in GeoGebra, the interactive figures may be found at bit.ly/2MibgaO or in the Video and Resource Library of MyLab Math. These exercises are labeled with a special icon.
• Explaining Concepts: Discussion and Writing problems are marked by red numbers. These support class discussion, verbalization of mathematical ideas, and writing and research projects.
• REVISED – Expanded Retain Your Knowledge problems—While the focus of these problems remains the maintenance of students’ skills, in most sections problems preview skills students need to succeed in subsequent sections or in calculus. 
• NEW – Key to Exercise Types helps users navigate the features of the exercise sets with a key at the bottom of the first page of each section’s exercises.

Reviewing for exams and quizzes

• Chapter Reviews offer a variety of convenient tools for reference and review.
• You Should be Able To… is a list of every objective, by section, with corresponding practice exercises. Doing the recommended exercises allows students to master the key concepts. 
• Review Exercises provide comprehensive review and practice of key skills matched to the Learning Objectives for each section. 
• Chapter Tests contain 15-20 problems that can help students prepare for in-class exams. For additional help, they can watch an instructor work out full solutions on the Chapter Test Prep Video in MyLab Math.
• Cumulative Review problem sets appear at the end of every chapter after Chapter 1. 
• NEW – College Algebra Essential Video Series covers the essential topics a college algebra student needs to understand to be successful in this course.  Videos can be assigned in a MyLab Math homework assignment to remind students of the crucial content before students begin on their exercises.

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 Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

• 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.
• NEW – Enhanced Sample Assignments are pre-made section-level assignments that address key concepts within the section and help keep previously learned skills fresh with Retain Your Knowledge questions. They are assignable and editable.
• NEW – Setup & Solve Exercises require students to show how they set up a problem as well as the solution, better mirroring what is required of them on tests. We have included both the “traditional” and Setup & Solve versions of exercise within MyLab to provide you with more options for assessing students.
• Concept and Vocabulary exercises are now assignable in MyLab Math as reading quizzes.
• 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 – Integrated Review content and assessments help you provide students with just the remediation they need, when they need it. Integrated Review consists of:
• Skills Check Quizzes by chapter assess the prerequisite skills students need for that chapter.
• Personalized Skills Review Homework is generated for each student based on the results of the Skills Check Quiz to provide students with help on the prerequisite skills they are lacking. Students receive just the help they need—no more, no less.
• Algebra Review eText, Exercises, Videos, and Worksheets are offered for students who need more help (or for co-requisite courses). There’s no need to go elsewhere for remediation.
• NEW  – Mindset material in MyLab Math encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities — so often a major hurdle for math students.

• NEW – Personal Inventory Assessments are a collection of online exercises designed to promote self-reflection and engagement in students. These 33 assessments include topics such as a Stress Management Assessment, Diagnosing Poor Performance and Enhancing Motivation, and Time Management Assessment. 

• 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. 
• NEW – Interactive Figures (formerly Guided Visualizations) – The suite of Interactive Figures has been expanded to support teaching and learning. The figures (created in GeoGebra by author Michael Sullivan III) illustrate key concepts and allow manipulation. They have been designed to be used in lecture as well as by students independently.
• 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.

Improve student results: When you teach with MyLab, student performance often improves. That’s why instructors have chosen MyLab for over 15 years, touching the lives of over 50 million students. 

Table of Contents

1. Review
   • R.1 Real Numbers
   • R.2 Algebra Essentials
   • R.3 Geometry Essentials
   • R.4 Polynomials
   • R.5 Factoring Polynomials
   • R.6 Synthetic Division
   • R.7 Rational Expressions
   • R.8 n th Roots; Rational Exponents
2. Graphs, Equations, and Inequalities
   • 1.1 Graphing Utilities; Introduction to Graphing Equations
   • 1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
   • 1.3 Quadratic Equations
   • 1.4 Complex Numbers; Quadratic Equations in the Complex Number System
   • 1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
   • 1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
   • 1.7 Solving Inequalities
3. Graphs
   • 2.1 The Distance and Midpoint Formulas
   • 2.2 Intercepts: Symmetry; Graphing Key Equations
   • 2.3 Lines
   • 2.4 Circles
   • 2.5 Variation
4. Functions and Their Graphs
   • 3.1 Functions
   • 3.2 The Graph of a Function
   • 3.3 Properties of Functions
   • 3.4 Library of Functions; Piecewise-defined Functions
   • 3.5 Graphing Techniques: Transformations
   • 3.6 Mathematical Models: Building Functions
5. Linear and Quadratic Functions
   • 4.1 Properties of Linear Functions and Linear Models
   • 4.2 Building Linear Models from Data
   • 4.3 Quadratic Functions and Their Properties
   • 4.4 Build Quadratic Models from Verbal Descriptions and from Data
   • 4.5 Inequalities Involving Quadratic Functions
6. Polynomial and Rational Functions
   • 5.1 Polynomial Functions
   • 5.2 The Graph of a Polynomial Function; Models
   • 5.3 The Real Zeroes of a Polynomial Function
   • 5.4 Complex Zeroes: Fundamental Theorem of Algebra
   • 5.5 Properties of Rational Functions
   • 5.6 The Graph of a Rational Function
   • 5.7 Polynomial and Rational Inequalities
7. Exponential and Logarithmic Functions
   • 6.1 Composite Functions
   • 6.2 One-to-One Functions; Inverse Functions
   • 6.3 Exponential Functions
   • 6.4 Logarithmic Functions
   • 6.5 Properties of Logarithms
   • 6.6 Logarithmic and Exponential Equations
   • 6.7 Financial Models
   • 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
   • 6.9 Building Exponential, Logarithmic, and Logistic Models from Data
8. Trigonometric Functions
   • 7.1 Angles and Their Measure
   • 7.2 Right Triangle Trigonometry
   • 7.3 Computing the Values of Trigonometric Functions of Acute Angles
   • 7.4 Trigonometric Functions of Any Angle
   • 7.5 Unit Circle Approach; Properties of the Trigonometric Functions
   • 7.6 Graphs of the Sine and Cosine Functions
   • 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
   • 7.8 Phase Shift; Sinusoidal Curve Fitting
9. Analytic Trigonometry
   • 8.1 The Inverse Sine, Cosine, and Tangent Functions
   • 8.2 The Inverse Trigonometric Functions (Continued)
   • 8.3 Trigonometric Equations
   • 8.4 Trigonometric Identities
   • 8.5 Sum and Difference Formulas
   • 8.6 Double-angle and Half-angle Formulas
   • 8.7 Product-to-Sum and Sum-to-Product Formulas
10. Applications of Trigonometric Functions
    • 9.1 Applications Involving Right Triangles
    • 9.2 The Law of Sines
    • 9.3 The Law of Cosines
    • 9.4 Area of a Triangle
    • 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
11. Polar Coordinates; Vectors
    • 10.1 Polar Coordinates
    • 10.2 Polar Equations and Graphs
    • 10.3 The Complex Plane; De Moivre’s Theorem
    • 10.4 Vectors
    • 10.5 The Dot Product
12. Analytic Geometry
    • 11.1 Conics
    • 11.2 The Parabola
    • 11.3 The Ellipse
    • 11.4 The Hyperbola
    • 11.5 Rotation of Axes; General Form of a Conic
    • 11.6 Polar Equations of Conics
    • 11.7 Plane Curves and Parametric Equations
13. Systems of Equations and Inequalities
    • 12.1 Systems of Linear Equations: Substitution and Elimination
    • 12.2 Systems of Linear Equations: Matrices
    • 12.3 Systems of Linear Equations: Determinants
    • 12.4 Matrix Algebra
    • 12.5 Partial Fraction Decomposition
    • 12.6 Systems of Nonlinear Equations
    • 12.7 Systems of Inequalities
    • 12.8 Linear Programming
14. Sequences; Induction; the Binomial Theorem
    • 13.1 Sequences
    • 13.2 Arithmetic Sequences
    • 13.3 Geometric Sequences; Geometric Series
    • 13.4 Mathematical Induction
    • 13.5 The Binomial Theorem
15. Counting and Probability
    • 14.1 Counting
    • 14.2 Permutations and Combinations
    • 14.3 Probability

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 recently retiring. 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. He 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 is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer, who tries to spend as much of his limited free time as possible on the golf course.