Precalculus Essentials

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 9
Acknowledgments......Page 13
To the Student......Page 18
About the Author......Page 19
C......Page 20
F......Page 21
L......Page 22
R......Page 23
T......Page 24
Y......Page 25
P: Prerequisites: Fundamental Concepts of Algebra......Page 26
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers......Page 27
P.2 Exponents and Scientific Notation......Page 45
P.3 Radicals and Rational Exponents......Page 57
P.4 Polynomials......Page 73
P.5 Factoring Polynomials......Page 83
Mid-Chapter Check Point......Page 95
P.6 Rational Expressions......Page 97
P.7 Equations......Page 113
P.8 Modeling with Equations......Page 134
P.9 Linear Inequalities and Absolute Value Inequalities......Page 151
Summary, Review, and Test......Page 166
Review Exercises......Page 167
Chapter P: Test......Page 170
1 Functions and Graphs......Page 174
1.1 Graphs and Graphing Utilities......Page 175
1.2 Basics of Functions and Their Graphs......Page 187
1.3 More on Functions and Their Graphs......Page 206
1.4 Linear Functions and Slope......Page 226
1.5 More on Slope......Page 242
Mid-Chapter Check Point......Page 253
1.6 Transformations of Functions......Page 254
1.7 Combinations of Functions; Composite Functions......Page 271
1.8 Inverse Functions......Page 286
1.9 Distance and Midpoint Formulas; Circles......Page 298
1.10 Modeling with Functions......Page 307
Summary, Review, and Test......Page 321
Review Exercises......Page 324
Chapter 1 Test......Page 330
2 Polynomial and Rational Functions......Page 332
2.1 Complex Numbers......Page 333
2.2 Quadratic Functions......Page 341
2.3 Polynomial Functions and Their Graphs......Page 360
2.4 Dividing Polynomials; Remainder and Factor Theorems......Page 378
2.5 Zeros of Polynomial Functions......Page 391
Mid-Chapter Check Point......Page 406
2.6 Rational Functions and Their Graphs......Page 407
2.7 Polynomial and Rational Inequalities......Page 428
2.8 Modeling Using Variation......Page 441
Summary, Review, and Test......Page 451
Review Exercises......Page 454
Chapter 2 Test......Page 458
Cumulative Review Exercises (Chapters P–2)......Page 460
3 Exponential and Logarithmic Functions......Page 462
3.1 Exponential Functions......Page 463
3.2 Logarithmic Functions......Page 477
3.3 Properties of Logarithms......Page 492
Mid-Chapter Check Point......Page 502
3.4 Exponential and Logarithmic Equations......Page 503
3.5 Exponential Growth and Decay; Modeling Data......Page 518
Summary, Review, and Test......Page 534
Review Exercises......Page 536
Chapter 3 Test......Page 540
Cumulative Review Exercises (Chapters P–3)......Page 541
4 Trigonometric Functions......Page 542
4.1 Angles and Radian Measure......Page 543
4.2 Trigonometric Functions: The Unit Circle......Page 560
4.3 Right Triangle Trigonometry......Page 575
4.4 Trigonometric Functions of Any Angle......Page 589
Mid-Chapter Check Point......Page 602
4.5 Graphs of Sine and Cosine Functions......Page 603
4.6 Graphs of Other Trigonometric Functions......Page 624
4.7 Inverse Trigonometric Functions......Page 638
4.8 Applications of Trigonometric Functions......Page 654
Summary, Review, and Test......Page 665
Review Exercises......Page 668
Cumulative Review Exercises (Chapters P–4)......Page 672
5 Analytic Trigonometry......Page 674
5.1 Verifying Trigonometric Identities......Page 675
5.2 Sum and Difference Formulas......Page 686
5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas......Page 697
Mid-Chapter Check Point......Page 708
5.4 Product-to-Sum and Sum-to-Product Formulas......Page 709
5.5 Trigonometric Equations......Page 718
Summary, Review, and Test......Page 731
Review Exercises......Page 732
Cumulative Review Exercises (Chapters P–5)......Page 734
6 Additional Topics in Trigonometry......Page 736
6.1 The Law of Sines......Page 737
6.2 The Law of Cosines......Page 749
6.3 Polar Coordinates......Page 758
6.4 Graphs of Polar Equations......Page 770
Mid-Chapter Check Point......Page 781
6.5 Complex Numbers in Polar Form; DeMoivre’s Theorem......Page 782
6.6 Vectors......Page 795
6.7 The Dot Product......Page 810
Summary, Review, and Test......Page 820
Review Exercises......Page 823
Chapter 6 Test......Page 825
Cumulative Review Exercises (Chapters P–6)......Page 826
Appendix A: Where Did That Come From? Selected Proofs......Page 828
Appendix B: The Transition From Precalculus to Calculus......Page 832
Answers to Selected Exercises......Page 834
A......Page 910
C......Page 911
D......Page 912
E......Page 913
F......Page 914
G......Page 915
I......Page 916
L......Page 917
M......Page 918
O......Page 919
P......Page 920
R......Page 921
S......Page 923
T......Page 925
V......Page 926
Z......Page 927
Credits......Page 928