Precalculus: Enhanced with Graphing Utilities

by Sullivan, Michael; Sullivan, Michael

• ISBN13: 9780131490925
• ISBN10: 0131490923
• Edition: 4th
• Format: Hardcover
• Copyright: 2009-01-01
• Publisher: Prentice Hall

Summary

This is the number one, best selling graphing-required version of Mike Sullivan's precalculus series. It is used by thousands of students and hundreds of instructors because, simply, "IT WORKS." "IT WORKS for both instructors and students because Mike Sullivan, after twenty-five years of teaching, knows exactly what students need to do to succeed in a math class and he therefore emphasizes and organizes his text around the fundamentals; preparing, practicing, and reviewing. Students who prepare (read the book, practice their skills learned in previous math classes), practice (work the math focusing on the fundamental and important mathematical concepts), and review (study key concepts and review for quizzes and tests) succeed in class. Instructors appreciate this emphasis as it supports their teaching goals to help their students succeed as well as appreciate the fact that this dependable text retains its best features- - accuracy, precision, depth, strong student support, and abundant exercises, while substantially updating content and pedagogy. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus.

Table of Contents

Preface to the Instructor	xiii
List of Applications	xix
Photo Credits	xxiii
To the Student	xxiv
Graphs	1	(54)
Rectangular Coordinates; Graphing Utilities	2	(9)
Graphs of Equations in Two Variables	11	(13)
Solving Equations in One Variable Using a Graphing Utility	24	(3)
Lines	27	(17)
Circles	44	(11)
Chapter Review	51	(3)
Chapter Test	54	(1)
Chapter Projects	54	(1)
Functions and Their Graphs	55	(94)
Functions	56	(15)
The Graph of a Function	71	(9)
Properties of Functions	80	(13)
Linear Functions and Models	93	(14)
Library of Functions; Piecewise-defined Functions	107	(11)
Graphing Techniques: Transformations	118	(12)
Mathematical Models: Constructing Functions	130	(19)
Chapter Review	138	(7)
Chapter Test	145	(1)
Chapter Projects	146	(1)
Cumulative Review	147	(2)
Polynomial and Rational Functions	149	(98)
Quadratic Functions and Models	150	(20)
Polynomial Functions and Models	170	(16)
Properties of Rational Functions	186	(12)
The Graph of a Rational Function; Inverse and Joint Variation	198	(14)
Polynomial and Rational Inequalities	212	(7)
The Real Zeros of a Polynomial Function	219	(14)
Complex Zeros: Fundamental Theorem of Algebra	233	(14)
Chapter Review	238	(6)
Chapter Test	244	(1)
Chapter Projects	245	(1)
Cumulative Review	246	(1)
Exponential and Logarithmic Functions	247	(108)
Composite Functions	248	(8)
One-to-One Functions; Inverse Functions	256	(15)
Exponential Functions	271	(16)
Logarithmic Functions	287	(13)
Properties of Logarithms	300	(9)
Logarithmic and Exponential Equations	309	(6)
Compound Interest	315	(9)
Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay	324	(13)
Building Exponential, Logarithmic, and Logistic Models from Data	337	(18)
Chapter Review	345	(7)
Chapter Test	352	(1)
Chapter Projects	353	(1)
Cumulative Review	353	(2)
Trigonometric Functions	355	(92)
Angles and Their Measure	356	(14)
Trigonometric Functions: Unit Circle Approach	370	(18)
Properties of the Trigonometric Functions	388	(14)
Graphs of the Sine and Cosine Functions	402	(17)
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions	419	(6)
Phase Shift: Sinusoidal Curve Fitting	425	(22)
Chapter Review	437	(6)
Chapter Test	443	(2)
Chapter Projects	445	(1)
Cumulative Review	446	(1)
Analytic Trigonometry	447	(70)
The Inverse Sine, Cosine, and Tangent Functions	448	(12)
The Inverse Trigonometric Functions (continued)	460	(5)
Trigonometric Identities	465	(8)
Sum and Difference Formulas	473	(10)
Double-angle and Half-angle Formulas	483	(10)
Product-to-Sum and Sum-to-Product Formulas	493	(3)
Trigonometric Equations (I)	496	(7)
Trigonometric Equations (II)	503	(14)
Chapter Review	511	(3)
Chapter Test	514	(1)
Chapter Projects	515	(1)
Cumulative Review	516	(1)
Applications of Trigonometric Functions	517	(54)
Right Triangle Trigonometry; Applications	518	(13)
The Law of Sines	531	(12)
The Law of Cosines	543	(6)
Area of a Triangle	549	(6)
Simple Harmonic Motion; Damped Motion; Combining Waves	555	(16)
Chapter Review	564	(4)
Chapter Test	568	(1)
Chapter Projects	569	(1)
Cumulative Review	570	(1)
Polar Coordinates; Vectors	571	(80)
Polar Coordinates	572	(9)
Polar Equations and Graphs	581	(19)
The Complex Plane; De Moivre's Theorem	600	(8)
Vectors	608	(12)
The Dot Product	620	(8)
Vectors in Space	628	(10)
The Cross Product	638	(13)
Chapter Review	645	(4)
Chapter Test	649	(1)
Chapter Projects	650	(1)
Cumulative Review	650	(1)
Analytic Geometry	651	(74)
Conics	652	(1)
The Parabola	653	(11)
The Ellipse	664	(11)
The Hyperbola	675	(14)
Rotation of Axes; General Form of a Conic	689	(9)
Polar Equations of Conics	698	(7)
Plane Curves and Parametric Equations	705	(20)
Chapter Review	719	(3)
Chapter Test	722	(1)
Chapter Projects	723	(1)
Cumulative Review	723	(2)
Systems of Equations and Inequalities	725	(106)
Systems of Linear Equations: Substitution and Elimination	726	(15)
Systems of Linear Equations: Matrices	741	(17)
Systems of Linear Equations: Determinants	758	(10)
Matrix Algebra	768	(17)
Partial Fraction Decomposition	785	(8)
Systems of Nonlinear Equations	793	(11)
Systems of Inequalities	804	(11)
Linear Programming	815	(16)
Chapter Review	823	(5)
Chapter Test	828	(1)
Chapter Project	829	(1)
Cumulative Review	830	(1)
Sequences; Induction; The Binomial Theorem	831	(44)
Sequences	832	(12)
Arithmetic Sequences	844	(6)
Geometric Sequences: Geometric Series	850	(9)
Mathematical Induction	859	(4)
The Binomial Theorem	863	(12)
Chapter Review	870	(2)
Chapter Test	872	(1)
Chapter Project	873	(1)
Cumulative Review	874	(1)
Counting and Probability	875	(34)
Sets and Counting	876	(6)
Permutations and Combinations	882	(11)
Probability	893	(16)
Chapter Review	904	(3)
Chapter Test	907	(1)
Chapter Project	908	(1)
Cumulative Review	908	(1)
A Preview of Calculus: The Limit, Derivative, and Integral of a Function	909	(42)
Finding Limits Using Tables and Graphs	910	(5)
Algebra Techniques for Finding Limits	915	(8)
One-sided Limits; Continuous Functions	923	(7)
The Tangent Problem; The Derivative	930	(8)
The Area Problem; The Integral	938	(13)
Chapter Review	946	(3)
Chapter Test	949	(1)
Chapter Project	950	(1)
Appendix Review	951
A.1. Algebra Review	951	(10)
A.2. Geometry Review	961	(5)
A.3. Polynomials and Rational Expressions	966	(11)
A.4. Polynomial Division; Synthetic Division	977	(7)
A.5. Solving Equations	984	(16)
A.6. Complex Numbers; Quadratic Equations in the Complex Number System	1000	(9)
A.7. Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs	1009	(11)
A.8. Interval Notation; Solving Inequalities	1020	(12)
A.9. nth Roots; Rational Exponents; Radical Equations	1032
Answers	1	(1)
Index	1