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Elementary and Intermediate Algebra: Graphs and Models, 4th Edition

By Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Published by Pearson

Published Date: Dec 27, 2010


The Bittinger Graphs and Models Series helps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math. The authors use a variety of tools and techniques—including graphing calculators, multiple approaches to problem solving, and interactive features—to engage and motivate all types of learners.

Table of Contents



1. Introduction to Algebraic Expressions
1.1 Introduction to Algebra Models
1.2 The Commutative, Associative, and Distributive Laws
1.3 Fraction Notation
1.4 Positive and Negative Real Numbers
Mid-Chapter Review
1.5 Addition of Real Numbers
1.6 Subtraction of Real Numbers
1.7 Multiplication and Division of Real Numbers
1.8 Exponential Notation and Order of Operations


2. Equations, Inequalities, and Problem Solving
2.1 Solving Equations
2.2 Using the Principles Together
2.3 Formulas
Mid-Chapter Review
2.4 Applications with Percent
2.5 Problem Solving
2.6 Solving Inequalities
2.7 Solving Applications with Inequalities


3. Introduction to Graphing and Functions
3.1 Reading Graphs, Plotting Points, and Scaling Graphs
3.2 Graphing Equations
3.3 Linear Equations and Intercepts
3.4 Rates
3.5 Slope
Mid-Chapter Review
3.6 Slope-Intercept Form
3.7 Point-Slope Form; Introduction to Curve
3.8 Functions


4. Systems of Equations in Two Variables
4.1 Systems of Equations and Graphing
Solutions of Systems
4.2 Systems of Equations and Substitution
4.3 Systems of Equations and Elimination
Mid-Chapter Review
4.4 More Applications Using Systems
4.5 Solving Equations by Graphing


5. Polynomials
5.1 Exponents and Their Properties
5.2 Negative Exponents and Scientific Notation
5.3 Polynomials and Polynomial Functions
5.4 Addition and Subtraction of Polynomials
5.5 Multiplication of Polynomials
5.6 Special Products
Mid-Chapter Review
5.7 Polynomials in Several Variables
5.8 Division of Polynomials
5.9 The Algebra of Functions


6. Polynomial Factorizations and Equations
6.1 Introduction to Polynomial Factorizations and Equations
6.2 Trinomials of the Type x2 + bx + c
6.3 Trinomials of the Type ax2 + bx + c
Mid-Chapter Review
6.4 Perfect-Square Trinomials and Differences of Squares
6.5 Sums or Differences of Cubes
6.6 Factoring: A General Strategy
6.7 Applications of Polynomial Equations
Cumulative Review: Chapters 1-6


7. Rational Expressions, Equations, and Functions
7.1 Rational Expressions and Functions
7.2 Multiplication and Division
7.3 Addition, Subtraction, and Least Common Denominators
7.4 Addition and Subtraction with Unlike Denominators
Mid-Chapter Review
7.5 Complex Rational Expressions
7.6 Rational Equations
7.7 Applications Using Rational Equations and Proportions
7.8 Formulas, Applications, and Variation


8. Inequalities
8.1 Graphical Solutions and Compound Inequalities
8.2 Absolute-Value Equations and Inequalities
Mid-Chapter Review
8.3 Inequalities in Two Variables
8.4 Polynomial Inequalities and Rational Inequalities


9. More on Systems
9.1 Systems of Equations in Three Variables
9.2 Solving Applications: Systems of Three Equations
9.3 Elimination Using Matrices
Mid-Chapter Review
9.4 Determinants and Cramer's Rule
9.5 Business and Economics Applications
Cumulative Review: Chapters 1-9


10. Exponents and Radical Functions
10.1 Radical Expressions, Functions, and Models
10.2 Rational Numbers as Exponents
10.3 Multiplying Radical Expressions
10.4 Dividing Radical Expressions
10.5 Expressions Containing Several Radical Terms
Mid-Chapter Review
10.6 Solving Radical Equations
10.7 The Distance Formula, the Midpoint Formula, and Other Applications
10.8 The Complex Numbers


11. Quadratic Functions and Equations
11.1 Quadratic Equations
11.2 The Quadratic Formula
11.3 Studying Solutions of Quadratic Equations
11.4 Applications Involving Quadratic Equations
11.5 Equations Reducible to Quadratic
Mid-Chapter Review
11.6 Quadratic Functions and Their Graphs
11.7 More About Graphing Quadratic Functions
11.8 Problem Solving and Quadratic Functions


12. Exponential Functions and Logarithmic Functions
12.1 Composite Functions and Inverse Functions
12.2 Exponential Functions
12.3 Logarithmic Functions
12.4 Properties of Logarithmic Functions
Mid-Chapter Review
12.5 Natural Logarithms and Changing Bases
12.6 Solving Exponential and Logarithmic Equations
12.7 Applications of Exponential and Logarithmic Functions
Cumulative Review Chapters 1-12


13. Conic Sections
13.1 Conic Sections: Parabolas and Circles
13.2 Conic Sections: Ellipses
13.3 Conic Sections: Hyperbolas
Mid-Chapter Review
13.4 Nonlinear Systems of Equations

14. Sequences, Series, and the Binomial Theorem
14.1 Sequences and Series
14.2 Arithmetic Sequences and Series
14.3 Geometric Sequences and Series
Mid-Chapter Review
14.4 The Binomial Theorem
Cumulative Review: Chapters 1-14


R. Elementary Algebra Review
R.1 Introduction to Algebraic Expressions
R.2 Equations, Inequalities, and Problem Solving
R.3 Introduction to Graphing and Functions
R.4 Systems of Equations in Two Variables
R.5 Polynomials
R.6 Polynomial Factorizations and Equations


Photo Credits
Index of Applications

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