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With a visual, graphical approach that emphasizes connections among concepts, this text helps students make the most of their study time. The authors show how different mathematical ideas are tied together through their zeros, solutions, and x-intercepts theme; side-by-side algebraic and graphical solutions; calculator screens; and examples and exercises. By continually reinforcing the connections among various mathematical concepts as well as different solution methods, the authors lead students to the ultimate goal of mastery and success in class.
Chapter R: Basic Concepts of Algebra
R.1 The Real-Number System
R.2 Integer Exponents, Scientific Notation, and Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
R.4 Factoring
R.5 Rational Expressions
R.6 Radical Notation and Rational Exponents
R.7 The Basics of Equation Solving
Chapter 1: Graphs, Functions, and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
1.4 Equations of Lines and Modeling
1.5 More on Functions
1.6 The Algebra of Functions
1.7 Symmetry and Transformations
Chapter 2: Functions, Equations, and Inequalities
2.1 Linear Equations, Functions, and Models
2.2 The Complex Numbers
2.3 Quadratic Equations, Functions, and Models
2.4 Analyzing Graphs of Quadratic Functions
2.5 More Equation Solving
2.6 Solving Linear Inequalities
Chapter 3: Polynomial and Rational Functions
3.1 Polynomial Functions and Models
3.2 Graphing Polynomial Functions
3.3 Polynomial Division; The Remainder and Factor Theorems
3.4 Theorems about Zeros of Polynomial Functions
3.5 Rational Functions
3.6 Polynomial and Rational Inequalities
3.7 Variation and Applications
Chapter 4: Exponential and Logarithmic Functions
4.1 Inverse Functions
4.2 Exponential Functions and Graphs
4.3 Logarithmic Functions and Graphs
4.4 Properties of Logarithmic Functions
4.5 Solving Exponential and Logarithmic Equations
4.6 Applications and Models: Growth and Decay; Compound Interest
Chapter 5: The Trigonometric Functions
5.1 Trigonometric Function of Acute Angles
5.2 Applications of Right Triangles
5.3 Trigonometric Functions of Any Angle
5.4 Radians, Arc Length, and Angular Speed
5.5 Circular Functions: Graphs and Properties
5.6 Graphs of Transformed Sine and Cosine Functions
Chapter 6: Trigonometric Identities, Inverse Functions, and Equations
6.1 Identities: Pythagorean and Sum and Difference
6.2 Identities: Cofunction, Double-Angle, and Half-Angle
6.3 Proving Trigonometric Identities
6.4 Inverses of the Trigonometric Functions
6.5 Solving Trigonometric Equations
Chapter 7: Applications of Trigonometry
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Complex Numbers: Trigonometric Form
7.4 Polar Coordinates and Graphs
7.5 Vectors and Applications
7.6 Vector Operations
Chapter 8: Systems of Equations and Matrices
8.1 Systems of Equations in Two Variables
8.2 Systems of Equations in Three Variables
8.3 Matrices and Systems of Equations
8.4 Matrix Operations
8.5 Inverses of Matrices
8.6 Determinants and Cramer's Rule
8.7 Systems of Inequalities and Linear Programming
8.8 Partial Fractions
Chapter 9: Analytic Geometry Topics
9.1 The Parabola
9.2 The Circle and the Ellipse
9.3 The Hyperbola
9.4 Nonlinear Systems of Equations and Inequalities
9.5 Rotation of Axes
9.6 Polar Equations of Conics
9.7 Parametric Equations
Chapter 10: Sequences, Series, and Combinatorics
10.1 Sequences and Series
10.2 Arithmetic Sequences and Series
10.3 Geometric Sequences and Series
10.4 Mathematical Induction
10.5 Combinatorics: Permutations
10.6 Combinatorics: Combinations
10.7 The Binomial Theorem
10.8 Probability
Appendix Basic Concepts of Geometry
With a visual, graphical approach that emphasizes connections among concepts, this text helps students make the most of their study time. The authors show how different mathematical ideas are tied together through their zeros, solutions, and x-intercepts theme; side-by-side algebraic and graphical solutions; calculator screens; and examples and exercises. By continually reinforcing the connections among various mathematical concepts as well as different solution methods, the authors lead students to the ultimate goal of mastery and success in class.
Table of Contents
Chapter R: Basic Concepts of Algebra
R.1 The Real-Number System
R.2 Integer Exponents, Scientific Notation, and Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
R.4 Factoring
R.5 Rational Expressions
R.6 Radical Notation and Rational Exponents
R.7 The Basics of Equation Solving
Chapter 1: Graphs, Functions, and Models
1.1 Introduction to Graphing
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
1.4 Equations of Lines and Modeling
1.5 More on Functions
1.6 The Algebra of Functions
1.7 Symmetry and Transformations
Chapter 2: Functions, Equations, and Inequalities
2.1 Linear Equations, Functions, and Models
2.2 The Complex Numbers
2.3 Quadratic Equations, Functions, and Models
2.4 Analyzing Graphs of Quadratic Functions
2.5 More Equation Solving
2.6 Solving Linear Inequalities
Chapter 3: Polynomial and Rational Functions
3.1 Polynomial Functions and Models
3.2 Graphing Polynomial Functions
3.3 Polynomial Division; The Remainder and Factor Theorems
3.4 Theorems about Zeros of Polynomial Functions
3.5 Rational Functions
3.6 Polynomial and Rational Inequalities
3.7 Variation and Applications
Chapter 4: Exponential and Logarithmic Functions
4.1 Inverse Functions
4.2 Exponential Functions and Graphs
4.3 Logarithmic Functions and Graphs
4.4 Properties of Logarithmic Functions
4.5 Solving Exponential and Logarithmic Equations
4.6 Applications and Models: Growth and Decay; Compound Interest
Chapter 5: The Trigonometric Functions
5.1 Trigonometric Function of Acute Angles
5.2 Applications of Right Triangles
5.3 Trigonometric Functions of Any Angle
5.4 Radians, Arc Length, and Angular Speed
5.5 Circular Functions: Graphs and Properties
5.6 Graphs of Transformed Sine and Cosine Functions
Chapter 6: Trigonometric Identities, Inverse Functions, and Equations
6.1 Identities: Pythagorean and Sum and Difference
6.2 Identities: Cofunction, Double-Angle, and Half-Angle
6.3 Proving Trigonometric Identities
6.4 Inverses of the Trigonometric Functions
6.5 Solving Trigonometric Equations
Chapter 7: Applications of Trigonometry
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Complex Numbers: Trigonometric Form
7.4 Polar Coordinates and Graphs
7.5 Vectors and Applications
7.6 Vector Operations
Chapter 8: Systems of Equations and Matrices
8.1 Systems of Equations in Two Variables
8.2 Systems of Equations in Three Variables
8.3 Matrices and Systems of Equations
8.4 Matrix Operations
8.5 Inverses of Matrices
8.6 Determinants and Cramer's Rule
8.7 Systems of Inequalities and Linear Programming
8.8 Partial Fractions
Chapter 9: Analytic Geometry Topics
9.1 The Parabola
9.2 The Circle and the Ellipse
9.3 The Hyperbola
9.4 Nonlinear Systems of Equations and Inequalities
9.5 Rotation of Axes
9.6 Polar Equations of Conics
9.7 Parametric Equations
Chapter 10: Sequences, Series, and Combinatorics
10.1 Sequences and Series
10.2 Arithmetic Sequences and Series
10.3 Geometric Sequences and Series
10.4 Mathematical Induction
10.5 Combinatorics: Permutations
10.6 Combinatorics: Combinations
10.7 The Binomial Theorem
10.8 Probability
Appendix Basic Concepts of Geometry