Table of Contents
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
Mid-Chapter Check Point
P.5 Factoring Polynomials
P.6 Rational Expressions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER P TEST
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
Mid-Chapter Check Point
1.6 Other Types of Equations
1.7 Linear Inequalities and Absolute Value Inequalities
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 1 TEST
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
Mid-Chapter Check Point
2.5 Transformations of Functions
2.6 Combinations of Functions; Composite Functions
2.7 Inverse Functions
2.8 Distance and Midpoint Formulas; Circles
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 2 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2)
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
Mid-Chapter Check Point
3.5 Rational Functions and Their Graphs
3.6 Polynomial and Rational Inequalities
3.7 Modeling Using Variation
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 3 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3) 410
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
Mid-Chapter Check Point
4.4 Exponential and Logarithmic Equations
4.5 Exponential Growth and Decay; Modeling Data
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 4 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4)
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
Mid-Chapter Check Point
5.5 Systems of Inequalities
5.6 Linear Programming
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 5 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5)
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
Mid-Chapter Check Point
6.4 Multiplicative Inverses of Matrices and Matrix Equations
6.5 Determinants and Cramer's Rule
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 6 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-6)
7. Conic Sections
7.1 The Ellipse
7.2 The Hyperbola
Mid-Chapter Check Point
7.3 The Parabola
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 7 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-7)
8. Sequences, Induction, and Probability
8.1 Sequences and Summation Notation
8.2 Arithmetic Sequences
8.3 Geometric Sequences and Series
Mid-Chapter Check Point
8.4 Mathematical Induction
8.5 The Binomial Theorem
8.6 Counting Principles, Permutations, and Combinations
8.7 Probability
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 8 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-8)
Appendix: Where Did That Come From? Selected Proofs
Answers to Selected Exercises
Subject Index
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