Precalculus: A Narrative Approach Book

Chapter 1: Polynomials
1.1. Definitions and Examples of Polynomials
1.2. Addition and Subtraction of Polynomials
1.3. Multiplication of Polynomials
1.4. Division of Polynomials
1.5. Factoring Polynomials
1.5.1. Greatest Common Factors
1.5.2. Difference (and Sum) of 2 Squares
1.5.3. Difference and Sum of 2 Cubes
1.5.4. Quadratic Trinomials
1.5.5. Polynomials with Four Terms
1.5.6. Putting It All Together

Chapter 2: Rational Expressions
2.1. Definitions and Simplifying Rational Expressions
2.2. Multiplication and Division of Rational Expressions
2.3. Addition and Subtraction of Rational Expressions
2.4. Simplifying Mixed Quotients

Chapter 3: Radical Expressions
3.1. Square Roots
3.2. Cube Roots
3.3. Radicals in General
3.4. Rational Exponents

Chapter 4: Using the Calculator
4.1. Approximating a Decimal
4.2. Evaluating Numerical Expressions

Chapter 5: Solving Equations in One Variable
5.1. Linear Equations and Literal Equations
5.2. Quadratic Equations and Complex Numbers
5.2.1 Quadratic Equations with Real Roots
5.2.2 Complex Numbers
5.3. Radical Equations
5.4. Polynomial Equations
5.5. Rational Equations
5.6. Quadratic-Like Equations

Chapter 6: Solving Inequalities in One Variable
6.1. Linear Inequalities
6.1.1 Basic Set Theory
6.1.2 Notations Used With Inequalities and Their Interpretations
6.1.3 Properties of Inequalities
6.1.4 Solving Linear Inequalities
6.2. Polynomial Inequalities
6.3. Rational Inequalities

Chapter 7: Absolute Value
7.1. Definition, Examples and Properties of Absolute Value
7.2. Absolute Value Equations
7.3. Absolute Value Inequalities

Chapter 8: Equations in Two Variables and Their Graphs
8.1. Preliminary Definitions
8.2. The Cartesian Plane and Analytic Geometry
8.3. Linear Equations in Two Variables and Their Graphs
8.4. Graphs of Non-Linear Equations in Two Variables
8.5. Tools For Graphing Equations in Two Variables

Chapter 9: Functions
9.1. Definitions, Notations and Computations
9.2. Finding the Domain of a Function
9.3. Obtaining Information from the Graph of a Function
9.4. Even and Odd Functions
9.5. Average Rate of Change

Chapter 10: Graphing Techniques for Functions
10.1. The Basic Functions and Piecewise-Defined Functions
10.2. The Shifting Techniques
10.3. The Stretching and Compressing Techniques
10.4. Reflections About The x-Axis and y-Axis
10.5. Combining the Graphing Techniques

Chapter 11: Algebra of Functions
11.1. Addition, Subtraction, Multiplication and Division of Functions
11.2. The Composition of Functions
11.3. Inverse Functions
11.3.1. The Inverse of a Function
11.3.2. One-to-One Functions
11.3.3. Inverse Functions and Their Properties
11.3.4. Finding the Inverse of a One-To-One Function
11.3.5. The Graph of a One-To-One Function and its Inverse
11.4. Constructing Functions: Mathematical Modeling

Chapter 12: Polynomial Functions
12.1. Quadratic Functions
12.2. Power Functions
12.3. Polynomial Functions

Chapter 13: Rational Functions
13.1. Definition and Domain of a Rational Function
13.2. Graphs of Some Basic Rational Functions
13.3. Vertical, Horizontal and Oblique Asymptotes
13.4. Graphing Rational Functions

Chapter 14: Exponential Functions and Logarithmic Functions
14.1. Exponential Functions
14.1.1. Review of Exponents and Using the Calculator
14.1.2. The Graph of f (x) = ax, where <i>a > 1
14.1.3. The Graph of f (x) = ax, where 0 <i>< a < </i>1
14.1.4. Graphing Exponential Functions Using Graphing Techniques
14.1.5. The Number ‘e’
14.1.6. Applications of Exponential Functions
14.2. Logarithmic Functions
14.2.1. Definition of a Logarithmic Function
14.2.2. The Graph of a Logarithmic Function
14.2.3. Algebraic Properties of a Logarithmic Function
14.3. Logarithmic and Exponential Equations
14.3.1. Logarithmic Equations
14.3.2. Exponential Equations
14.4. Exponential Growth and Decay Models

Chapter 15: Trigonometric Functions
15.1. Angles and Their Measure
15.2. Right Triangle Trigonometry
15.3. Trigonometry of Any Angle
15.4. The Unit Circle Approach to Trigonometry; Functional Properties
15.5. Graphing Trigonometric Functions

Solutions to ‘Try These’ Examples
Solutions to Odd Numbered Exercises