# College Algebra, 7th edition

Published by Pearson (January 1, 2017) © 2018

**Robert F. Blitzer**Miami Dade College

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**Engage students with the mathematical world around them.****UPDATED! Outstanding applications**from diverse fields are the centerpiece of this series, drawing from the author’s unique background in behavioral science. Students stay engaged when they see the context and understand the relevance of math. In this new edition, the author continues to raise the bar with new applications throughout that are relevant to college students, including student-loan debt, grade inflation, political orientation of college freshmen, sleep hours of college students, and the number of hours college students study per week.**Chapter Opening and Section-Opening Scenarios**begin every chapter and section with a unique application of mathematics in students’ lives outside the classroom. The often humorous tone of these openers is intended to help fearful and reluctant students overcome their negative perceptions about math. These scenarios are revisited throughout the chapter in examples, discussions, and exercises.**Blitzer Bonuses**provide historical, interdisciplinary, and otherwise interesting connections to the algebra being studied, showing students that math is an interesting and dynamic discipline. New to this edition, these are brought to life in in a new video series and related assignments.

**Support students of all majors in their goal to be successful--in this course and beyond.****NEW! Achieving Success**boxes appear at the end of many sections in Chapters 1 through 5 with strategies for persistence and success in college mathematics courses.**NEW! “Retaining the Concepts”**section exercises focus on objectives that appeared previously in the text, to ensure students continue to apply and maintain mastery of the material. If students are not certain how to solve one of these, they can refer to the specific section and worked example provided next to each exercise.**Learning Objectives,**framed in the context of a student question (What am I supposed to learn?), are clearly stated at the beginning of each section. These objectives help students recognise and focus on the section’s most important ideas. The objectives are restated in the margin at their point of use.**Voice balloons**offer the support and guidance of an instructor’s voice. These translate algebraic ideas into everyday English, clarify problem-solving procedures, present alternative ways of understanding concepts, and connect problem solving to concepts students have already learned.**Check Point Examples**follow a similar matched problem and offer students the opportunity to test their understanding of the example by working a similar exercise. The answers to the Check Points are provided in the answer section.**Detailed Worked-Out Examples**make the purpose of the example clear. Examples are clearly written and provide students with detailed step-by-step solutions. No steps are omitted and each step is thoroughly explained to the right of the mathematics.**Great Question!**takes the content from each Study Tip and presents it in the context of a student question. Answers to the questions offer suggestions for problem solving, point out common errors to avoid, and provide informal hints and suggestions.**Integration of Technology Using Graphic and Numerical Approaches to Problems**are side-by-side features in the technology boxes that show how graphing utilities verify and visualise algebraic results. Even for those not using graphing utilities, these displays will help students understand different approaches to problem solving.**Discovery boxes,**found

**About the Book**

**Engage students with the mathematical world around them.****UPDATED! Outstanding applications**from diverse fields are the centerpiece of this series, drawing from the author’s unique background in behavioral science. Students stay engaged when they see the context and understand the relevance of math. In this new edition, the author continues to raise the bar with new applications throughout that are relevant to college students, including student-loan debt, grade inflation, political orientation of college freshmen, sleep hours of college students, and the number of hours college students study per week.

**Support students of all majors in their goal to be successful--in this course and beyond.****Achieving Success**boxes appear at the end of many sections in Chapters 1 through 5 with strategies for persistence and success in college mathematics courses.**“Retaining the Concepts”**section exercises focus on objectives that appeared previously in the text, to ensure students continue to apply and maintain mastery of the material. If students are not certain how to solve one of these, they can refer to the specific section and worked example provided next to each exercise.

**Help students to study efficiently and apply their understanding with extensive and varied exercise sets****Learning Guide**. Organized by the textbook's learning objectives, the Learning Guide is available as a print supplement to help students make the most of their textbook for test preparation. Activities are now included to give students an opportunity to discover and reinforce the concepts in an active learning environment and are ideal for group work in class.**Brief Review**boxes summarize the most critical prerequisite mathematical skills students should know in order to master the chapter’s objectives. This feature appears whenever a particular skill is first needed and eliminates the need for reteaching that skill. For more detail, students are referred to the appropriate section and objective in a previous chapter where the topic is fully developed.**Retaining the Concepts**exercises are a chance for students to review previously covered objectives in order to help maintain their mastery of the material and keep skills fresh. Beginning with Chapter 2 each Exercise Set contains three review exercises under the header “Retaining the Concepts.” These exercises are also available to assign through MyLab™ Math.

**Content and Organizational Changes in the Seventh Edition:**

- Section P.1 (Algebraic Expressions, Mathematical Models, and Real Numbers) follows an example on the cost of attending college (Example 2) with a new Blitzer Bonus, “Is College Worthwhile?”
- Section P.6 (Rational Expressions) uses the least common denominator to combine rational expressions with different denominators, including expressions having no common factors in their denominators.
- Section 1.1 (Graphing and Graphing Utilities) contains a new example of a graph with more than one
*x*-intercept (Example 5(d)). - Section 1.4 (Complex Numbers) includes a new example on dividing complex numbers where the numerator is of the form
*bi*(Example 3). (This is then followed by an example picked up from the Sixth Edition where the numerator is of the form*a*+*bi.*) - Section 1.5 (Quadratic Equations) provides a step-by-step procedure for solving quadratic equations by completing the square. This procedure forms the framework for the solutions in Examples 4 and 5.
- Section 1.5 (Quadratic Equations) contains an example on the quadratic formula (Example 6) where the formula is used to solve a quadratic equation with rational solutions, an equation that students can also solve by factoring.
- Section 1.5 (Quadratic Equations) has a new application of the Pythagorean Theorem (Example 11) involving HDTV screens. The example is followed by a new Blitzer Bonus, “Screen Math.”
- Section 1.6 (Other Types of Equations) includes an example on solving an equation quadratic in form (Example 8), (
*x*- 5)^{2}^{2}+ 3(*x*^{2}- 5) - 10 = 0, where*u*is a binomial (*u*=*x*^{2}- 5). - Section 2.2 (More on Functions and Their Graphs) contains a new discussion on graphs with three forms of symmetry (Examples 2 and 3) before presenting even and odd functions. A new example (Example 4) addresses identifying even or odd functions from graphs.
- Section 2.3 (Linear Functions and Slope) includes a new Blitzer Bonus, “Slope and Applauding Together.”
- Section 2.7 (Inverse Functions) replaces an example on finding the inverse of
*f(x)*= 5/*x*+ 4 with an example on finding the inverse of*f(x)*=*x*+ 2/*x*- 3 (Example 4), a function with two occurrences of*x*. - Section 3.5 (Rational Functions and Their Graphs opens with a discussion of college students and video games. This is revisited in a new example (Example 9, “Putting the Video-Game Player Inside the Game”) involving the Oculus Rift, a virtual reality headset that enables users to experience video games as immersive three-dimensional environments.
- Section 5.1 (Systems of Linear Equations in Two Variables) contains a new discussion on problems involving mixtures, important for many STEM students. A new example (Example 8) illustrates the procedure for solving a mixture problem.
- Section 6.1 (Matrix Solutions to Linear Systems) has a new opening example (Example 1) showing the details on how to write an augmented matrix.
- Section 7.1 (The Ellipse) includes a new example (Example 5) showing the details on graphing an ellipse centered at (
*h, k*) by completing the square. - Section 7.3 (The Parabola) adds a new objective on identifying conics of the for
*Ax*+^{2}*Cy*+^{2}*Dx*+*Ey*+*F*= 0 without completing the square, supported by an example (Example 7). - Section 8.2 (Arithmetic Sequences) contains a new example (Example 3) on writing the general term of an arithmetic sequence.
- Section 8.7 (Probability) uses the popular lottery games Powerball (Example 5) and Mega Millions (Exercises 27—30) as applications of probability and combinations.

**Also available with MyLab Math.**

MyLab™ Math 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. The new edition continues to expand the comprehensive auto-graded exercise options. In addition, MyLab Math includes new options designed to help students of all levels and majors to stay engaged and succeed in the course.

**Students enter the course with widely varying skill levels, so MyLab Math includes personalized support and targeted practice to help all students succeed.****Skill Builder**offers adaptive practice that is designed to increase a student’s ability to complete assignments. By monitoring student performance on 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.**Workspace Assignments**allow students to work through an exercise step-by-step, adjusting to the path each student takes and allowing them to show their mathematical reasoning as they progress, receiving feedback when and where they need it most. When accessed via a mobile device, Workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.

**Engage students with the mathematical world around them, and develop their visualization skills to strengthen their understanding of the concepts.****Blitzer Bonus Videos**bring the applications from the text to life, helping students make visual connections to algebra and the world around them. These are ideal for the classroom, or they can be assigned to students in MyLab Math as media assignments or through the new exercises that assess conceptual understanding of the videos.**Guided Visualizations**are interactive figures that help students visualize the concepts through directed explorations and purposeful manipulation. They encourage active learning, critical thinking, and conceptual understanding, and they can be assigned as homework with correlating exercises. Additional Exploratory Exercises are available to help students think more conceptually about the figures and provide an excellent framework for group projects or lecture discussions. For easy access, Guided Visualizations are available in the Multimedia Library and are HTML based, making them compatible with iPad and tablet devices.

**Support students in their desire to be successful--in this course and beyond.****Retaining the Concepts**exercises are a chance for students to review previously covered objectives in order to help maintain their mastery of the material and keep skills fresh. Beginning with Chapter 2 each Exercise Set contains three review exercises under the header “Retaining the Concepts.” These exercises are also available to assign through MyLab Math.**Video Program**includes fresh, interactive videos that walk students through the concepts from every objective of the text. The videos provide an active learning environment where students can work at their own pace.

**Easier course set-up for instructors****Enhanced Sample Assignments**make course set-up easier by giving instructors a starting point for each chapter. Each assignment, carefully curated for this specific text, with selections from Bob Blitzer, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic.

**Foster in-class student engagement and peer-to-peer learning****UPDATED! Learning Guide**, organized by the textbook's learning objectives, is available as a print supplement to help students make the most of their textbook for test preparation. Learning Guides are now included to give students an opportunity to discover and reinforce the concepts in an active learning environment and are ideal for group work in class**Learning Catalytics**helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking.^{™ }- Upload a full PowerPoint
^{®}deck for easy creation of slide questions. - Team names are no longer case sensitive.
- Help your students develop critical thinking skills.
- Monitor responses to find out where your students are struggling.
- Rely on real-time data to adjust your teaching strategy.
- Automatically group students for discussion, teamwork, and peer-to-peer learning.

**P. Prerequisites: Fundamental Concepts of Algebra**

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.2 Exponents and Scientific Notation

P.3 Radicals and Rational Exponents

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions

**1. Equations and Inequalities**

1.1 Graphs and Graphing Utilities

1.2 Linear Equations and Rational Equations

1.3 Models and Applications

1.4 Complex Numbers

1.5 Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities and Absolute Value Inequalities

**2. Functions and Graphs**

2.1 Basics of Functions and Their Graphs

2.2 More on Functions and Their Graphs

2.3 Linear Functions and Slope

2.4 More on Slope

2.5 Transformations of Functions

2.6 Combinations of Functions; Composite Functions

2.7 Inverse Functions

2.8 Distance and Midpoint Formulas; Circles

**3. Polynomial and Rational Functions**

3.1 Quadratic Functions

3.2 Polynomial Functions and Their Graphs

3.3 Dividing Polynomials; Remainder and Factor Theorems

3.4 Zeros of Polynomial Functions

3.5 Rational Functions and Their Graphs

3.6 Polynomial and Rational Inequalities

3.7 Modeling Using Variation

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Exponential and Logarithmic Equations

4.5 Exponential Growth and Decay; Modeling Data

**5. Systems of Equations and Inequalities**

5.1 Systems of Linear Equations in Two Variables

5.2 Systems of Linear Equations in Three Variables

5.3 Partial Fractions

5.4 Systems of Nonlinear Equations in Two Variables

5.5 Systems of Inequalities

5.6 Linear Programming

**6. Matrices and Determinants**

6.1 Matrix Solutions to Linear Systems

6.2 Inconsistent and Dependent Systems and Their Applications

6.3 Matrix Operations and Their Applications

6.4 Multiplicative Inverses of Matrices and Matrix Equations

6.5 Determinants and Cramer's Rule

**7. Conic Sections**

7.1 The Ellipse

7.2 The Hyperbola

7.3 The Parabola

**8. Sequences, Induction, and Probability**

8.1 Sequences and Summation Notation

8.2 Arithmetic Sequences

8.3 Geometric Sequences and Series

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principles, Permutations, and Combinations

8.7 Probability

**Bob Blitzer** is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to College Algebra, Bob has written textbooks covering developmental mathematics, introductory algebra, intermediate algebra, trigonometry, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

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