Graphical Approach to Precalculus Book

Chapter 1 Linear Functions, Equations, and Inequalities

1.1 Real Numbers and the Rectangular Coordinate System

1.2 Introduction to Relations and Functions

1.3 Linear Functions

1.4 Equations of Lines and Linear Models

1.5 Linear Equations and Inequalities

1.6 Applications of Linear Functions

Chapter 2 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

2.4 Absolute Value Functions: Graphs, Equations, Inequalities, and Applications

2.5 Piecewise-Defined Functions

2.6 Operations and Composition

Chapter 3 Polynomial Functions

3.1 Complex Numbers

3.2 Quadratic Functions and Graphs

3.3 Quadratic Equations and Inequalities

3.4 Further Applications of Quadratic Functions and Models

3.5 Higher-Degree Polynomial Functions and Graphs

3.6 Topics in the Theory of Polynomial Functions (I)

3.7 Topics in the Theory of Polynomial Functions (II)

3.8 Polynomial Equations and Inequalities; Further Applications and Models

Chapter 4 Rational, Power, and Root Functions

4.1 Rational Functions and Graphs

4.2 More on Graphs of Rational Functions

4.3 Rational Equations, Inequalities, Applications, and Models

4.4 Functions Defined by Powers and Roots

4.5 Equations, Inequalities, and Applications Involving Root Functions

Chapter 5 Inverse, Exponential, and Logarithmic Functions

5.1 Inverse Functions

5.2 Exponential Functions

5.3 Logarithms and Their Properties

5.4 Logarithmic Functions

5.5 Exponential and Logarithmic Equations and Inequalities

5.6 Further Applications and Modeling with Exponential and Logarithmic Functions

Chapter 6 Analytic Geometry

6.1 Circles and Parabolas

6.2 Ellipses and Hyperbolas

6.3 Summary of Conic Sections

6.4 Parametric Equations

Chapter 7 Systems of Equations and Inequalities; Matrices

7.1 Systems of Equations

7.2 Solution of Linear Systems in Three Variables

7.3 Solution of Linear Systems by Row Transformations

7.4 Matrix Properties and Operations

7.5 Determinants and Cramer’s Rule

7.6 Solution of Linear Systems by Matrix Inverses

7.7 Systems of Inequalities and Linear Programming

7.8 Partial Fractions

Chapter 8 Trigonometric Functions and Applications

8.1 Angles and Their Measures

8.2 Trigonometric Functions and Fundamental Identities

8.3 Evaluating Trigonometric Functions

8.4 Applications of Right Triangles

8.5 The Circular Functions

8.6 Graphs of the Sine and Cosine Functions

8.7 Graphs of the Other Circular Functions

8.8 Harmonic Motion

Chapter 9 Trigonometric Identities and Equations

9.1 Trigonometric Identities

9.2 Sum and Difference Identities

9.3 Further Identities

9.4 The Inverse Circular Functions

9.5 Trigonometric Equations and Inequalities (I)

9.6 Trigonometric Equations and Inequalities (II)

Chapter 10 Applications of Trigonometry; Vectors

10.1 The Law of Sines

10.2 The Law of Cosines and Area Formulas

10.3 Vectors and Their Applications

10.4 Trigonometric (Polar) Form of Complex Numbers

10.5 Powers and Roots of Complex Numbers

10.6 Polar Equations and Graphs

10.7 More Parametric Equations

Chapter 11 Further Topics in Algebra

11.1 Sequences and Series

11.2 Arithmetric Sequences and Series

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

11.5 Mathematical Induction

11.6 Counting Theory

11.7 Probability

Chapter R Reference: Basic Algebraic Concepts

R.1 Review of Exponents and Polynomials

R.2 Review of Factoring

R.3 Review of Rational Expressions

R.4 Review of Negative and Rational Exponents

R.5 Review of Radicals

Appendix A Geometry Formulas

Appendix B Deciding Which Model Best Fits a Set of Data