Precalculus Essentials

by Blitzer, Robert F.

• ISBN13: 9780131090446
• ISBN10: 0131090445
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Prentice Hall

Summary

For courses in Precalculus. This text takes the same approach as the regular Blitzer Precalculus version, but has been condensed by deleting the last 5 chapters (Chapter 7 Systems of Equations and Inequalities; Chapter 8 Matrices and Determinants; Chapter 9 Conic Sections and Analytic Geometry; Chapter 10 Sequences, Induction, and Probability; Chapter 11 Introduction to Calculus). This text explores math the way it evolved: by describing real problems and how math explains them. It is interesting, lively (with applications you won't see in any other math book), and exceedingly clear. Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly. Students are strongly supported by a consistent pedagogical framework. A See it, Hear it, Try it? format consistently walks students through each and every example in just the same way that an instructor would teach this example in class. Blitzer liberally inserts voice balloons and annotations throughout the text helping clarify the more difficult concepts for students.

Table of Contents

Preface	x
To the Student	xiv
Applications Index	xxi
Prerequisites: Fundamental Concepts of Algebra	1	(114)
Real Numbers and Algebraic Expressions	2	(11)
Exponents and Scientific Notation	13	(9)
Radicals and Rational Exponents	22	(12)
Polynomials	34	(10)
Factoring Polynomials	44	(11)
Rational Expressions	55	(15)
Linear Equations	70	(14)
Quadratic Equations	84	(15)
Linear Inequalities	99	(16)
Summary	109	(1)
Review Exercises	110	(3)
Chapter P Test	113	(2)
Graphs, Functions, and Models	115	(130)
Graphs and Graphing Utilities	116	(8)
Lines and Slopes	124	(18)
Distance and Midpoint Formulas; Circles	142	(8)
Basics of Functions	150	(13)
Graphs of Functions	163	(21)
Transformations of Functions	184	(13)
Combinations of Functions; Composite Functions	197	(12)
Inverse Functions	209	(10)
Modeling with Functions	219	(26)
Summary	234	(2)
Review Exercises	236	(6)
Chapter 1 Test	242	(3)
Polynomial and Rational Functions	245	(110)
Complex Numbers	246	(7)
Quadratic Functions	253	(16)
Polynomial Functions and Their Graphs	269	(13)
Dividing Polynomials; Remainder and Factor Theorems	282	(10)
Zeros of Polynomial Functions	292	(13)
Rational Functions and Their Graphs	305	(21)
Polynomial and Rational Inequalities	326	(10)
Modeling Using Variation	336	(19)
Summary	347	(2)
Review Exercises	349	(4)
Chapter 2 Test	353	(1)
Cumulative Review Exercises	354	(1)
Exponential and Logarithmic Functions	355	(67)
Exponential Functions	356	(11)
Logarithmic Functions	367	(13)
Properties of Logarithms	380	(9)
Exponential and Logarithmic Equations	389	(11)
Modeling with Exponential and Logarithmic Functions	400	(22)
Summary	416	(1)
Review Exercises	417	(4)
Chapter 3 Test	421	(1)
Cumulative Review Exercises	421	(1)
Trigonometric Functions	422	(122)
Angles and Their Measure	423	(14)
Trigonometric Functions: The Unit Circle	437	(16)
Right Triangle Trigonometry	453	(11)
Trigonometric Functions of Any Angle	464	(11)
Graphs of Sine and Cosine Functions	475	(22)
Graphs of Other Trigonometric Functions	497	(12)
Inverse Trigonometric Functions	509	(16)
Applications of Trigonometric Functions	525	(19)
Summary	536	(3)
Review Exercises	539	(3)
Chapter 4 Test	542	(1)
Cumulative Review Exercises	543	(1)
Analytic Trigonometry	544	(54)
Verifying Trigonometric Identities	546	(9)
Sum and Difference Formulas	555	(10)
Double-Angle and Half-Angle Formulas	565	(11)
Product-to-Sum and Sum-to-Product Formulas	576	(8)
Trigonometric Equations	584	(14)
Summary	594	(1)
Review Exercises	595	(2)
Chapter 5 Test	597	(1)
Cumulative Review Exercises	597	(1)
Additional Topics in Trigonometry	598	(88)
The Law of Sines	598	(13)
The Law of Cosines	611	(8)
Polar Coordinates	619	(11)
Graphs of Polar Equations	630	(12)
Complex Numbers in Polar Form; DeMoivre's Theorem	642	(13)
Vectors	655	(14)
The Dot Product	669	(17)
Summary	678	(3)
Review Exercises	681	(3)
Chapter 6 Test	684	(1)
Cumulative Review Exercises	684	(2)
Shaded chapters available in Blitzer, Precalculus, 2nd ed.
Systems of Equations and Inequalities	686	(72)
Systems of Linear Equations in Two Variables	687	(19)
Systems of Linear Equations in Three Variables	706	(9)
Partial Fractions	715	(9)
Systems of Nonlinear Equations in Two Variables	724	(9)
Systems of Inequalities	733	(10)
Linear Programming	743	(15)
Summary	752	(1)
Review Exercises	753	(3)
Chapter 7 Test	756	(1)
Cumulative Review Exercises	757	(1)
Matrices and Determinants	758	(73)
Matrix Solutions to Linear Systems	759	(14)
Inconsistent and Dependent Systems and Their Applications	773	(9)
Matrix Operations and Their Applications	782	(15)
Multiplicative Inverses of Matrices and Matrix Equations	797	(15)
Determinants and Cramer's Rule	812	(19)
Summary	825	(1)
Review Exercises	826	(3)
Chapter 8 Test	829	(1)
Cumulative Review Exercises	829	(2)
Conic Sections and Analytic Geometry	831	(84)
The Ellipse	832	(13)
The Hyperbola	845	(16)
The Parabola	861	(13)
Rotation of Axes	874	(13)
Parametric Equations	887	(11)
Conic Sections in Polar Coordinates	898	(17)
Summary	909	(2)
Review Exercises	911	(2)
Chapter 9 Test	913	(1)
Cumulative Review Exercises	914	(1)
Sequences, Induction, and Probability	915	(85)
Sequences and Summation Notation	916	(11)
Arithmetic Sequences	927	(9)
Geometric Sequences	936	(14)
Mathematical Induction	950	(9)
The Binomial Theorem	959	(8)
Counting Principles, Permutations, and Combinations	967	(11)
Probability	978	(22)
Summary	991	(3)
Review Exercises	994	(3)
Chapter 10 Test	997	(1)
Cumulative Review Exercises	998	(2)
Introduction to Calculus	1000	(1)
Finding Limits Using Tables and Graphs	1001	(10)
Finding Limits Using Properties of Limits	1011	(12)
One-Sided Limits; Continuous Functions	1023	(12)
Introduction to Derivatives	1035	(14)
Summary	1049	(1)
Review Exercises	1050	(2)
Chapter 11 Test	1052	(1)
Cumulative Review Exercises	1053
Appendix Where Did That Come From?
Selected Proofs	1	(1)
Answers to Selected Exercises	1	(1)
Subject Index	1	(1)
Photo Credits	1