Precalculus : a problems-oriented approach

Front cover......Page 1
Title page......Page 2
Copyrights......Page 3
Contents......Page 8
1.1 Sets of Real Numbers......Page 18
1.2 Absolute Value......Page 23
1.3 Solving Equations (Review and Preview)......Page 27
1.4 Rectangular Coordinates. Visualizing Data......Page 35
1.5 Graphs and Graphing Utilities......Page 49
1.6 Equations of Lines......Page 60
1.7 Symmetry and Graphs. Circles......Page 74
2.1 Quadratic Equations: Theory and Examples......Page 97
2.2 Other Types of Equations......Page 108
2.3 Inequalities......Page 120
2.4 More on Inequalities......Page 130
3.1 The Definition of a Function......Page 146
3.2 The Graph of a Function......Page 162
3.3 Shapes of Graphs. Average Rate of Change......Page 176
3.4 Techniques in Graphing......Page 188
3.5 Methods of Combining Functions. Iteration......Page 199
3.6 Inverse Functions......Page 211
4.1 Linear Functions......Page 230
4.2 Quadratic Functions......Page 246
4.3 Using Iteration to Model Population Growth (Optional Section)......Page 263
4.4 Setting Up Equations That Define Functions......Page 277
4.5 Maximum and Minimum Problems......Page 289
4.6 Polynomial Functions......Page 304
4.7 Rational Functions......Page 321
5 Exponential and Logarithmic Functions......Page 342
5.1 Exponential Functions......Page 344
5.2 The Exponential Function y = e(sup[x])......Page 353
5.3 Logarithmic Functions......Page 364
5.4 Properties of Logarithms......Page 378
5.5 Equations and Inequalities with Logs and Exponents......Page 388
5.6 Compound Interest......Page 399
5.7 Exponential Growth and Decay......Page 411
6.1 Trigonometric Functions of Acute Angles......Page 440
6.2 Algebra and the Trigonometric Functions......Page 454
6.3 Right-Triangle Applications......Page 462
6.4 Trigonometric Functions of Angles......Page 476
6.5 Trigonometric Identities......Page 489
7.1 Radian Measure......Page 504
7.2 Radian Measure and Geometry......Page 513
7.3 Trigonometric Functions of Real Numbers......Page 523
7.4 Graphs of the Sine and Cosine Functions......Page 538
7.5 Graphs of y = A sin(Bx - C) and y = A cos(Bx - C)......Page 555
7.6 Simple Harmonic Motion......Page 571
7.7 Graphs of the Tangent and the Reciprocal Functions......Page 577
8.1 The Addition Formulas......Page 594
8.2 The Double-Angle Formulas......Page 606
8.3 The Product-to-Sum and Sum-to-Product Formulas......Page 616
8.4 Trigonometric Equations......Page 624
8.5 The Inverse Trigonometric Functions......Page 636
9.1 The Law of Sines and the Law of Cosines......Page 662
9.2 Vectors in the Plane: A Geometric Approach......Page 678
9.3 Vectors in the Plane: An Algebraic Approach......Page 688
9.4 Parametric Equations......Page 701
9.5 Introduction to Polar Coordinates......Page 711
9.6 Curves in Polar Coordinates......Page 722
10.1 Systems of Two Linear Equations in Two Unknowns......Page 738
10.2 Gaussian Elimination......Page 752
10.3 Matrices......Page 766
10.4 The Inverse of a Square Matrix......Page 780
10.5 Determinants and Cramer’s Rule......Page 793
10.6 Nonlinear Systems of Equations......Page 806
10.7 Systems of Inequalities......Page 814
11.1 The Basic Equations......Page 826
11.2 The Parabola......Page 834
11.3 Tangents to Parabolas (Optional Section)......Page 848
11.4 The Ellipse......Page 850
11.5 The Hyperbola......Page 865
11.6 The Focus–Directrix Property of Conics......Page 876
11.7 The Conics in Polar Coordinates......Page 884
11.8 Rotation of Axes......Page 889
12 Roots of Polynomial Equations......Page 907
12.1 The Complex Number System......Page 908
12.2 Division of Polynomials......Page 915
12.3 The Remainder Theorem and the Factor Theorem......Page 922
12.4 The Fundamental Theorem of Algebra......Page 931
12.5 Rational and Irrational Roots......Page 943
12.6 Conjugate Roots and Descartes’s Rule of Signs......Page 951
12.7 Introduction to Partial Fractions......Page 958
12.8 More About Partial Fractions......Page 965
13.1 Mathematical Induction......Page 982
13.2 The Binomial Theorem......Page 988
13.3 Introduction to Sequences and Series......Page 998
13.4 Arithmetic Sequences and Series......Page 1008
13.5 Geometric Sequences and Series......Page 1019
13.6 DeMoivre’s Theorem......Page 1024
A.1 Significant Digits......Page 1038
A.2 Properties of the Real Numbers......Page 1041
A.3 √2 is Irrational......Page 1044
B.1 Review of Integer Exponents......Page 1045
B.2 Review of nth Roots......Page 1051
B.3 Review of Rational Exponents......Page 1058
B.4 Review of Factoring......Page 1062
B.5 Review of Fractional Expressions......Page 1068
Answers......Page 1074
Index......Page 1169
ENHANCED WEB ASSIGN......Page 1185
CONTENTS......Page 1187
Login to WebAssign......Page 1189
Logout......Page 1191
Using Access Codes......Page 1192
Customizing Your Home Page......Page 1194
Changing Your Email Address......Page 1195
Accessing an Assignment......Page 1196
Using the Assignment Page......Page 1198
Numerical Questions......Page 1201
Numerical Questions with Units......Page 1202
Numerical Questions with Significant Figures......Page 1203
Math Notation: Using the MathPad......Page 1204
Math Notation: Using the Keyboard......Page 1205
Introduction......Page 1206
Drawing Graph Objects......Page 1207
Selecting Graph Objects......Page 1208
Using Fractions or Decimals as Coordinates......Page 1209
Specifying a Region with a Fill for Inequalities......Page 1210
Erasing Everything on Your Graph......Page 1211
Example: Graphing Question......Page 1212
Communication......Page 1213
GRADES......Page 1214
TECHNICAL TIPS......Page 1215