Precalculus: Enhanced with Graphing Utilities, 9th edition

Michael Sullivan
, Michael Sullivan

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The proven approach of Sullivan and Sullivan, highly experienced math instructors, focuses you on the fundamental skills you’ll need to succeed in your course: prepare for class, practice with homework, and review the concepts.  Precalculus: Enhanced with Graphing Utilities fully integrates graphing utilities into topics, allowing you to explore mathematical concepts and encounter ideas usually studied in later courses. Many examples show solutions using algebra side by side with graphing techniques. The text offers a review chapter before covering the traditional precalculus topics of functions and their graphs, polynomial and rational functions, and exponential and logarithmic functions. The trigonometric functions are introduced using a unit circle approach and show how it is related to the right triangle approach.

The 9th Edition is revised and refined throughout, with updated Desmos and screen captures as well as TI-84 Plus CE screens; updates exercise sets with timely and relevant scenarios; adds a new Highlighting Contemporary Mathematicians feature, and much more.

ISBN-13: 9780135372968

Subject: Precalculus, College Algebra & Trigonometry

Category: Precalculus

1. Graphs

1.1 Graphing Utilities; Introduction to Graphing Equations
1.2 The Distance and Midpoint Formulas
1.3 Intercepts; Symmetry; Graphing Key Equations
1.4 Solving Equations Using a Graphing Utility
1.5 Lines
1.6 Circles
Chapter Review
Chapter Test
Chapter Project

2. Functions and Their Graphs

2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions; Piecewise-defined Functions
2.5 Graphing Techniques: Transformations
2.6 Mathematical Models: Building Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

3. Linear and Quadratic Functions

3.1 Properties of Linear Functions and Linear Models
3.2 Building Linear Models from Data
3.3 Quadratic Functions and Their Properties
3.4 Build Quadratic Models from Verbal Descriptions and From Data
3.5 Inequalities Involving Quadratic Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

4. Polynomial and Rational Functions

4.1 Polynomial Functions and Models
4.2 The Graph of a Polynomial Function and Models
4.3 The Real Zeros of a Polynomial Function
4.4 Complex Zeros; Fundamental Theorem of Algebra
4.5 Properties of Rational Functions
4.6 The Graph of a Rational Function
4.7 Polynomial and Rational Inequalities
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

5. Exponential and Logarithmic Functions

5.1 Composite Functions
5.2 One-to-One Functions; Inverse Functions
5.3 Exponential Functions
5.4 Logarithmic Functions
5.5 Properties of Logarithms
5.6 Logarithmic and Exponential Equations
5.7 Financial Models
5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
5.9 Building Exponential, Logarithmic, and Logistic Models from Data
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

6. Trigonometric Functions

6.1 Angles, Arc Length, and Circular Motion
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Sinusoidal Curve Fitting
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

7. Analytic Trigonometry

7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions (Continued)
7.3 Trigonometric Equations
7.4 Trigonometric Identities
7.5 Sum and Difference Formulas
7.6 Double-angle and Half-angle Formulas
7.7 Product-to-Sum and Sum-to-Product Formulas
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

8. Applications of Trigonometric Functions

8.1 Right Triangle Trigonometry; Applications
8.2 The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

9. Polar Coordinates; Vectors

9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; DeMoivre's Theorem
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

10. Analytic Geometry

10.1 Conics
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
10.5 Rotation of Axes; General Form of a Conic
10.6 Polar Equations of Conics
10.7 Plane Curves and Parametric Equations
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

11. Systems of Equations and Inequalities

11.1 Systems of Linear Equations: Substitution and Elimination
11.2 Systems of Linear Equations: Matrices
11.3 Systems of Linear Equations: Determinants
11.4 Matrix Algebra
11.5 Partial Fraction Decomposition
11.6 Systems of Nonlinear Equations
11.7 Systems of Inequalities
11.8 Linear Programming
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

12. Sequences; Induction; The Binomial Theorem

12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences; Geometric Series
12.4 Mathematical Induction
12.5 The Binomial Theorem
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

13. Counting and Probability

13.1 Counting
13.2 Permutations and Combinations
13.3 Probability
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

14. A Preview of Calculus: The Limit, Derivative, and Integral of a Fraction

14.1 Investigating Limits Using Tables and Graphs
14.2 Algebraic Techniques for Finding Limits
14.3 One-sided Limits; Continuity
14.4 The Tangent Problem; The Derivative
14.5 The Area Problem; The Integral
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects

Appendix A: Review

A.1 Algebra Essentials
A.2 Geometry Essentials
A.3 Polynomials
A.4 Synthetic Division
A.5 Rational Expressions
A.6 Solving Equations
A.7 Complex Numbers; Quadratic Equations in the Complex Number System
A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
A.9 Interval Notation; Solving Inequalities
A.10 nth Roots; Rational Exponents