College Algebra: Graphs & Models

✍ Scribed by John W. Coburn; J.D. Herdlick

• Publisher: McGraw-Hill
• Year: 2011
• Tongue: English
• Leaves: 992
• Category: Library

✦ Synopsis

Three components contribute to a theme sustained throughout the Coburn-Herdlick Series: that of laying a firm foundation, building a solid framework, and providing strong connections. In the Graphs and Models texts, the authors combine their depth of experience with the conversational style and the wealth of applications that the Coburn-Herdlick texts have become known for. By combining a graphical approach to problem solving with algebraic methods, students learn how to relate their mathematical knowledge to the outside world. The authors use technology to solve the more true-to life equations, to engage more applications, and to explore the more substantial questions involving graphical behavior. Benefiting from the feedback of hundreds of instructors and students across the country, College Algebra: Graphs & Models emphasizes connections in order to improve the level of student engagement in mathematics and increase their chances of success in college algebra.

The launch of the Coburn/Herdlick Graphs and Models series provides a significant leap forward in terms of online course management with McGraw-Hill's new homework platform, Connect Math Hosted by ALEKS Corp. Math instructors served as digital contributors to choose the problems that will be available, authoring each algorithm and providing stepped out solutions that go into great detail and are focused on areas where students commonly make mistakes. From there, the ALEKS Corporation reviewed each algorithm to ensure accuracy. A unifying theme throughout the entire process was the involvement of the authors. Through each step, they provided feedback and guidance to the digital contributors to ensure that the content being developed digitally closely matched the textbook. The result is an online homework platform that provides superior content and feedback, allowing students to effectively learn the material being taught.

✦ Table of Contents

Title
Contents
R A Review of Basic Concepts and Skills
R.1 Algebraic Expressions and the Properties of Real Numbers
R.2 Exponents, Scientific Notation, and a Review of Polynomials
R.3 Solving Linear Equations and Inequalities
R.4 Factoring Polynomials and Solving Polynomial Equations by Factoring
R.5 Rational Expressions and Equations
R.6 Radicals, Rational Exponents, and Radical Equations
Overview of Chapter R: Prerequisite Definitions, Properties, Formulas, and Relationships
1 Relations, Functions, and Graphs
1.1 Rectangular Coordinates; Graphing Circles and Other Relations
1.2 Linear Equations and Rates of Change
1.3 Functions, Function Notation, and the Graph of a Function
Mid-Chapter Check
Reinforcing Basic Concepts: Finding the Domain and Range of a Relation from Its Graph
1.4 Linear Functions, Special Forms, and More on Rates of Change
1.5 Solving Equations and Inequalities Graphically; Formulas and Problem Solving
1.6 Linear Function Models and Real Data
Making Connections
Summary and Concept Review
Practice Test
Strengthening Core Skills: The Various Forms of a Linear Equation
Calculator Exploration and Discovery: Evaluating Expressions and Looking for Patterns
2 More on Functions
2.1 Analyzing the Graph of a Function
2.2 The Toolbox Functions and Transformations
2.3 Absolute Value Functions, Equations, and Inequalities
Mid-Chapter Check
Reinforcing Basic Concepts: Using Distance to Understand Absolute Value Equations and Inequalities
2.4 Basic Rational Functions and Power Functions; More on the Domain
2.5 Piecewise-Defined Functions
2.6 Variation: The Toolbox Functions in Action
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Studying Joint Variations
Strengthening Core Skills: Variation and Power Functions: y � kxp
Cumulative Review: Chapters R–2
3 Quadratic Functions and Operations on Functions
3.1 Complex Numbers
3.2 Solving Quadratic Equations and Inequalities
3.3 Quadratic Functions and Applications
Mid-Chapter Check
Reinforcing Basic Concepts: An Alternative Method for Checking Solutions to Quadratic Equations
3.4 Quadratic Models; More on Rates of Change
3.5 The Algebra of Functions
3.6 The Composition of Functions and the Difference Quotient
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Residuals, Correlation Coefficients, and Goodness of Fit
Strengthening Core Skills: Base Functions and Quadratic Graphs
Cumulative Review: Chapters R–3
4 Polynomial and Rational Functions
4.1 Synthetic Division; the Remainder and Factor Theorems
4.2 The Zeroes of Polynomial Functions
4.3 Graphing Polynomial Functions
Mid-Chapter Check
Reinforcing Basic Concepts: Approximating Real Zeroes
4.4 Graphing Rational Functions
4.5 Additional Insights into Rational Functions
4.6 Polynomial and Rational Inequalities
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Complex Zeroes, Repeated Zeroes, and Inequalities
Strengthening Core Skills: Solving Inequalities Using the Push Principle
Cumulative Review: Chapters R–4
5 Exponential and Logarithmic Functions
5.1 One-to-One and Inverse Functions
5.2 Exponential Functions
5.3 Logarithms and Logarithmic Functions
5.4 Properties of Logarithms
Mid-Chapter Check
Reinforcing Basic Concepts: Understanding Properties of Logarithms
5.5 Solving Exponential and Logarithmic Equations
5.6 Applications from Business, Finance, and Science
5.7 Exponential, Logarithmic, and Logistic Equation Models
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Investigating Logistic Equations
Strengthening Core Skills: The HerdBurn Scale — What’s Hot and What’s Not
Cumulative Review: Chapters R–5
6 Systems of Equations and Inequalities
6.1 Linear Systems in Two Variables with Applications
6.2 Linear Systems in Three Variables with Applications
Mid-Chapter Check
Reinforcing Basic Concepts: Window Size and Graphing Technology
6.3 Nonlinear Systems of Equations and Inequalities
6.4 Systems of Inequalities and Linear Programming
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Optimal Solutions and Linear Programming
Strengthening Core Skills: Understanding Why Elimination and Substitution “Work”
Cumulative Review: Chapters R–6
7 Matrices and Matrix Applications
7.1 Solving Linear Systems Using Matrices and Row Operations
7.2 The Algebra of Matrices
Mid-Chapter Check
Reinforcing Basic Concepts: More on Matrix Multiplication
7.3 Solving Linear Systems Using Matrix Equations
7.4 Applications of Matrices and Determinants: Cramer’s Rule, Partial Fractions, and More
7.5 Matrix Applications and Technology Use
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Cramer’s Rule
Strengthening Core Skills: Augmented Matrices and Matrix Inverses
Cumulative Review: Chapters R–7
8 Analytic Geometry and the Conic Sections
8.1 A Brief Introduction to Analytical Geometry
8.2 The Circle and the Ellipse
Mid-Chapter Check
Reinforcing Basic Concepts: More on Completing the Square
8.3 The Hyperbola
8.4 The Analytic Parabola; More on Nonlinear Systems
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Elongation and Eccentricity
Strengthening Core Skills: Ellipses and Hyperbolas with Rational/Irrational Values of a and b
Cumulative Review: Chapters R–8
9 Additional Topics in Algebra
9.1 Sequences and Series
9.2 Arithmetic Sequences
9.3 Geometric Sequences
9.4 Mathematical Induction
Mid-Chapter Check
Reinforcing Basic Concepts: Applications of Summation
9.5 Counting Techniques
9.6 Introduction to Probability
9.7 The Binomial Theorem
Making Connections
Summary and Concept Review
Practice Test
Calculator Exploration and Discovery: Infinite Series, Finite Results
Strengthening Core Skills: Probability, Quick-Counting, and Card Games
Cumulative Review: Chapters R–9
Appendix I The Language, Notation, and Numbers of Mathematics
Appendix II Geometry Review with Unit Conversions
Appendix III More on Synthetic Division
Appendix IV More on Matrices
Appendix V Deriving the Equation of a Conic
Appendix VI Proof Positive — A Selection of Proofs from College Algebra
Student Answer Appendix (SE only)
Photo Credits
Index