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Contents
Linear Functions, Equations, and Inequalities
1.1 Real Numbers and the Rectangular Coordinate System
1.2 Introduction to Relations and Functions
Reviewing Basic Concepts (Sections 1.1-1.2)
1.3 Linear Functions
1.4 Equations of Lines and Linear Models
Reviewing Basic Concepts (Sections 1.3-1.4)
1.5 Linear Equations and Inequalities
Unifying Linear Functions
1.6 Applications of Linear Functions
Reviewing Basic Concepts (Sections 1.5-1.6)
Summary
Review Exercises
Test
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
Reviewing Basic Concepts (Sections 2.1-2.3)
2.4 Absolute Value Functions
Unifying Absolute Value Functions
2.5 Piecewise-Defined Functions
2.6 Operations and Composition
Reviewing Basic Concepts (Sections 2.4-2.6)
Summary
Review Exercises
Test
Quadratic Functions
3.1 Complex Numbers
3.2 Quadratic Functions and Graphs
Reviewing Basic Concepts (Sections 3.1-3.2)
3.3 Quadratic Equations and Inequalities
Unifying Quadratic Functions
3.4 Applications of Quadratic Functions and Models
Reviewing Basic Concepts (Sections 3.3-3.4)
Summary
Review Exercises
Test
Polynomial Functions of Higher Degree
4.1 Graphs of Polynomial Functions
4.2 Topics in the Theory of Polynomial Functions (I)
Reviewing Basic Concepts (Sections 4.1-4.2)
4.3 Topics in the Theory of Polynomial Functions (II)
4.4 Polynomial Equations, Inequalities, Applications, and Models
Reviewing Basic Concepts (Sections 4.3-4.4)
Unifying Polynomial Functions
Summary
Review Exercises
Test
Rational, Power, and Root Functions
5.1 Rational Functions and Graphs (I)
5.2 Rational Functions and Graphs (II)
5.3 Rational Equations, Inequalities, Models, and Applications
5.4 Functions Defined by Powers and Roots
5.5 Equations, Inequalities, and Applications Involving Root Functions
Reviewing Basic Concepts (Sections 5.4-5.5)
Unifying Root Functions
Summary
Review Exercises
Test
Inverse, Exponential, and Logarithmic Functions
6.1 Inverse Functions
6.2 Exponential Functions
6.3 Logarithms and Their Properties
6.4 Logarithmic Functions
6.5 Exponential and Logarithmic Equations and Inequalities
6.6 Further Applications and Modeling with Exponential and Logarithmic Functions
Reviewing Basic Concepts (Sections 6.4-6.6)
Summary
Review Exercises
Test
Systems and Matrices
7.1 Systems of Equations
7.2 Solution of Linear Systems in Three Variables
7.3 Solution of Linear Systems by Row Transformations
Reviewing Basic Concepts (Sections 7.1-7.3)
7.4 Matrix Properties and Operations
7.5 Determinants and Cramer's Rule
7.6 Solution of Linear Systems by Matrix Inverses
Reviewing Basic Concepts (Sections 7.4-7.6)
7.7 Systems of Inequalities and Linear Programming
7.8 Partial Fractions
Reviewing Basic Concepts (Sections 7.7-7.8)
Summary
Review Exercises
Test
Conic Sections, Nonlinear Systems, and Parametric Equations
8.1 Circles Revisited and Parabolas
8.2 Ellipses and Hyperbolas
Reviewing Basic Concepts (Sections 8.1-8.2)
8.3 The Conic Sections and Nonlinear Systems
8.4 Introduction to Parametric Equations
Reviewing Basic Concepts (Sections 8.3-8.4)
Summary
Review Exercises
Test
Further Topics in Algebra
9.1 Sequences and Series
9.2 Arithmetic Sequences and Series
9.3 Geometric Sequences and Series
Reviewing Basic Concepts (Sections 9.1-9.3)
9.4 Counting Theory
9.5 The Binomial Theorem
Reviewing Basic Concepts (Sections 9.4-9.5)
9.6 Mathematical Induction
9.7 Probability
Reviewing Basic Concepts (Sections 9.6-9.7)
Summary
Review Exercises
Test
Review: Basic Algebraic Concepts
R.2 Review of Exponents and Polynomials
R.3 Review of Factoring
R.4 Review of Rational Expressions
R.5 Review of Negative and Rational Exponents
R.6 Review of Radicals
Test
Appendix: Formulas from Geometry
Instructor's Answers
Answers to Selected Exercises*
Index
*In the AIE, Instructor's Answers replaces Answers to Selected Exercises.
