Table of Contents
Introduction ix
The Flashcard App xi
1 Functions 1
Relations and Functions 2
Composition of Functions 6
Inverse Functions 8
2 Quadratic Functions 13
Solving Quadratic Equations 14
Complex Numbers 16
Graphing Quadratic Functions - Parabolas 22
Applications of Quadratic Functions 24
3 Polynomial Functions 31
Factoring Polynomials 32
Remainder and Factor Theorems 33
Synthetic Division 34
Graphing Polynomial Functions 37
Using Graphs to Factor Polynomials 41
Fundamental Theorem of Algebra 46
Polynomial Inequalities 49
Rational Root Theorem and Descartes Rule of Signs 51
Maximum and Minimum Values of Polynomial Functions 55
4 Rational Functions 63
Intercepts for the Graphs of Rational Functions 64
Discontinuities of Rational Functions 65
End Behavior for Rational Functions 70
Graphing Rational Functions 73
Maxima and Minima of Rational Functions 77
5 Conic Sections 83
Analyze and Graph Circles 85
Analyze and Graph Parabolas 86
Analyzing and Graphing Ellipses 91
Analyze and Graph Hyperbolas 100
Eccentricity 108
Solutions of Systems of Quadratic Equations 109
6 Exponential and Logarithmic Functions 118
Exponential Functions 119
Logarithmic Functions 125
Applications of Exponential and Logarithmic Functions 136
7 Sequences and Series 148
Sequences 149
Summation Notation 155
Arithmetic Series 157
Geometric Series 160
Mathematical Induction 167
8 Systems of Equations and Matrices 175
Matrices 175
An Introduction to Matrices 176
Solve Two Variable Linear Systems Using Cramer's Rule and Inverse Matrices 179
Solving Three or More Variable Linear Systems 188
Solving Systems of Linear Inequalities 191
9 Triangle Trigonometry 203
Right Triangle Trigonometry 204
Figuring Out the Area of a Triangle Using Trigonometry 210
Law of Sines 212
The Ambiguous Case 216
Law of Cosines 220
10 Trigonometric Functions 230
Unit Circle 231
The First Quadrant 231
Beyond the First Quadrant 234
Radian Measure 238
Trigonometric Identities 243
Proving Trigonometric Identities 246
11 Graphs and Applications of Trigonometric Functions 255
Graphs of Trigonometric Functions 256
Inverse Trigonometric Functions 270
Applying Trigonometric Functions 273
Solving Trigonometric Equations 276
12 Polar and Parametric Equations 289
Plotting Points on a Polar Coordinate Plane 290
Conversion Between Polar and Rectangular Coordinates 292
Graphs of Polar Equations 294
The Rose 296
The Cardioid 304
The Limaçon 305
The Lemniscate 310
Conic Sections in Polar Coordinates 311
Nonstandard Polar Curves 314
Conversion Between Polar and Rectangular Forms for a Function 319
Conversion Between Parametric and Function Forms 322
13 Complex Numbers 335
Polar Form of Complex Numbers 336
Multiplication and Division of Complex Numbers 338
Powers and Roots of Complex Numbers 340
Exponential Format 344
14 Introduction to Calculus 348
The Concept of a Limit 349
Evaluating Limits 351
Property of Limits 357
Continuity 360
Instantaneous Rates of Change 361
Differentiation Rules 364
Answer Key 375