College Algebra: Graphs & Models Graphs & Models

by Coburn, John; Herdlick, J.D. (John)

• ISBN13: 9780073519548
• ISBN10: 0073519545
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-01-25
• Publisher: McGraw-Hill Education

Summary

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

College Algebra: Graphs & Models

Chapter 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: Factoring Polynomials and Solving Polynomial Equations by Factoring

R.4: Rational Expressions and Equations

R.5: Radicals, Rational Exponents, and Radical Equations

Chapter 1: Functions and Graphs

1.1: Rectangular Coordinates, Graphing Circles and Other Relations

1.2: Functions, Function Notation, and the Graph of a Function

1.3: Linear Equations and Rates of Change

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 Models and Real Data

Chapter 2: Relations, 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

2.4: Rational and Radical Functions; More on the Domain

2.5: Piecewise-Defined Functions

2.6: Variation: The Toolbox Functions in Action

Chapter 3: Quadratic Functions and Operations on Functions

3.1: Complex Numbers

3.2: Solving Quadratic Equations and Inequalities

3.3: Quadratic Functions and Applications

3.4: Quadratic Models; More on Rates of Change

3.5: The Algebra of Functions

3.6: Composition of Functions and the Difference Quotient

Chapter 4: Polynomial and Rational Functions

4.1: Synthetic Division; the Remainder and Factor Theorems

4.2: The Zeros of Polynomial Functions

4.3: Graphing Polynomial Functions

4.4: Graphing Rational Functions

4.5: Additional Insights into Rational Functions

Chapter 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

5.5: Solving Exponential/Logarithmic Equations

5.6: Applications from Business, Finance, and Science

5.7: Exponential, Logarithmic, and Logistic Equation Models

Chapter 6: Systems of Equations and Inequalities

6.1: Linear Systems in Two Variables with Applications

6.2: Linear Systems in Three Variables with Applications

6.3: Nonlinear Systems of Equations and Inequalities

6.4: Systems of Inequalities and Linear Programming

Chapter 7: Matrices and Matrix Applications

7.1: Solving Linear Systems Using Matrices and Row Operations

7.2: The Algebra of Matrices

7.3: Solving Linear Systems Using Matrix Equations

7.4: Applications of Matrices and Determinants: Cramer’s rule, Partial Fractions, and More

Chapter 8: Analytic Geometry and the Conic Sections

8.1: A Brief Introduction to Analytic Geometry

8.2: The Circle and the Ellipse

8.3: The Hyperbola

8.4: The Analytic Parabola

Chapter 9: Additional Topics in Algebra

9.1: Sequences and Series

9.2: Arithmetic Sequences

9.3: Geometric Sequences

9.4: Mathematical Induction

9.5: Counting Techniques

9.6: Introduction to Probability

9.7: The Binomial Theorem

Appendices

The Language, Notation, and Numbers of Mathematics

Geometry Review with Unit Conversions

More on Synthetic Division

More on Matrices

Deriving the Equation of a Conic

Proof Positive - A Selection of Proofs from College Algebra