A graphical approach to college algebra
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Bibliographic Information
A graphical approach to college algebra
Addison-Wesley, c2011
5th ed
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Includes index
Description and Table of Contents
Description
A Graphical Approach to College Algebra illustrates how the graph of a function can be used to support the solutions of equations and inequalities involving the function. Beginning with linear functions in Chapter 1, the text uses a four-part process to analyze each type of function, starting first with the graph of the function, then the equation, the associated inequality of that equation, and ending with applications. The text covers all of the topics typically caught in a college algebra course, but with an organization that fosters students' understanding of the interrelationships among graphs, equations, and inequalities.
With the Fifth Edition, the text continues to evolve as it addresses the changing needs of today's students. Included are additional components to build skills, address critical thinking, solve applications, and apply technology to support traditional algebraic solutions, while maintaining its unique table of contents and functions-based approach. A Graphical Approach to College Algebra continues to incorporate an open design, with helpful features and a careful explanations of topics.
Table of Contents
- 1. Linear Functions, Equations, and Inequalities 1.1. Real Numbers and the Rectangular Coordinate System 1.2. Introduction to Relations and Functions 1.3. Linear Functions 1.4. Equations of Lines and Linear Models 1.5. Linear Equations and Inequalities 1.6. Applications of Linear Functions 2. Analysis of Graphs of Functions 2.1. Graphs of Basic Functions and Relations
- Symmetry 2.2. Vertical and Horizontal Shifts of Graphs 2.3. Stretching, Shrinking, and Reflecting Graphs 2.4. Absolute Value Functions 2.5. Piecewise-Defined Functions 2.6. Operations and Composition 3. Polynomial Functions 3.1. Complex Numbers 3.2. Quadratic Functions and Graphs 3.3. Quadratic Equations and Inequalities 3.4. Further Applications of Quadratic Functions and Models 3.5. Higher-Degree Polynomial Functions and Graphs 3.6. Topics in the Theory of Polynomial Functions (I) 3.7. Topics in the Theory of Polynomial Functions (II) 3.8. Polynomial Equations and Inequalities
- Further Applications and Models 4. Rational, Power, and Root Functions 4.1. Rational Functions and Graphs 4.2. More on Rational Functions and Graphs 4.3. Rational Equations, Inequalities, Models, and Applications 4.4. Functions Defined by Powers and Roots 4.5. Equations, Inequalities, and Applications Involving Root Functions 5. Inverse, Exponential, and Logarithmic Functions 5.1. Inverse Functions 5.2. Exponential Functions 5.3. Logarithms and Their Properties 5.4. Logarithmic Functions 5.5. Exponential and Logarithmic Equations and Inequalities 5.6. Further Applications and Modeling with Exponential and Logarithmic Functions 6. Analytic Geometry 6.1. Circles and Parabolas 6.2. Ellipses and Hyperbolas 6.3. Summary of Conic Sections 6.4. Parametric Equations 7. Systems of Equations and Inequalities
- Matrices 7.1. Systems of Equations 7.2. Solution of Linear Systems in Three Variables 7.3. Solution of Linear Systems by Row Transformations 7.4. Matrix Properties and Operations 7.5. Determinants and Cramer's Rule 7.6. Solution of Linear Systems by Matrix Inverses 7.7. Systems of Inequalities and Linear Programming 7.8. Partial Fractions 8. Further Topics in Algebra 8.1 Sequences and Series 8.2 Arithmetic Sequences and Series 8.3 Geometric Sequences and Series 8.4 Counting Theory 8.5 The Binomial Theorem 8.6 Mathematical Induction 8.7 Probability R. Reference: Basic Algebraic Concepts R.1. Review of Exponents and Polynomials R.2. Review of Factoring R.3. Review of Rational Expressions R.4. Review of Negative and Rational Exponents R.5. Review of Radicals Appendix: Geometry Formulas
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