Table of Contents
Preface ix
1 Graphs and the Graphing Calculator 1
Step 1 Review Linear Equations 1
Step 2 Meet the Parents 3
Step 3 Master the Fundamentals of Graphing 15
Step 4 Transform the Graphs 16
Step 5 Master Basic Calculator Skills 22
2 Functions 25
Step 1 Analyze Relations and Functions 25
Step 2 Perform Arithmetic of Functions 28
Step 3 Compose Functions 33
Step 4 Find Inverse Functions 39
3 Quadratic Functions 43
Step 1 Solve Quadratic Functions 43
Step 2 Explore Complex Numbers 46
Step 3 Graph Parabolas 49
Step 4 Apply What You've Learned 52
4 Polynomial Functions 55
Step 1 Factor Polynomials 55
Step 2 Use Synthetic Division to Find Zeros 58
Step 3 Use Long Division to Factor Polynomials 60
Step 4 Find the Zeros of Polynomial Functions 62
Step 5 Graph Polynomial Functions 65
5 Rational Functions 71
Step 1 Operate with Rational Expressions 71
Step 2 Deal with Discontinuities 76
Step 3 Examine End Behavior 78
Step 4 Find Intercepts 82
Step 5 Graph Rational Functions 83
6 Conic Sections 88
Step 1 Analyze and Graph Parabolas 88
Step 2 Analyze and Graph Ellipses 91
Step 3 Analyze and Graph Circles 93
Step 4 Analyze and Graph Hyperbolas 95
Step 5 Graph and Solve Quadratic Systems 101
7 Exponential and Logarithmic Functions 104
Step 1 Get to Know the Exponential Function 104
Step 2 Define the Logarithmic Function 106
Step 3 Learn to Use Properties of Logarithms 108
Step 4 Solve Exponential and Logarithmic Equations 112
Step 5 Explore Exponential Growth and Decay 117
8 Radical Functions 122
Step 1 Review Rules for Exponents 122
Step 2 Simplify Radicals and Rationalize Denominators 124
Step 3 Explore the Square Root and Cube Root Functions 126
9 Systems of Equations 130
Step 1 Review Two-Variable Linear Systems 130
Step 2 Solve Systems of Linear Equations in Three Variables 134
Step 3 Solve Nonlinear Systems 137
10 Matrices and Determinants 142
Step 1 Master Matrix Arithmetic 142
Step 2 Find Determinants 146
Step 3 Apply Cramer's Rule 148
Step 4 Find Inverse Matrices 151
Step 5 Solve Systems by Inverse Matrices 156
11 Review Right Triangle Trigonometry 159
Step 1 Review Right Triangle-Trigonometry 159
Step 2 Use Trigonometry to Find Areas 162
Step 3 Use the Law of Cosines to Extend to Nonright Triangles 164
Step 4 Apply the Law of Sines 168
12 Trigonometric Functions 174
Step 1 Expand Your Concept of Angles 174
Step 2 Learn the Unit Circle 176
Step 3 Define Trigonometric Functions 180
Step 4 Explore Inverse Trigonometric Functions 186
Step 5 Verify Identities 188
Step 6 Use Identities 193
Step 7 Solve Trigonometric Equations 194
13 Polar and Parametric Equations 196
Step 1 Plot Points in the Polar Coordinate System 196
Step 2 Convert Coordinates Between Systems 198
Step 3 Graph Polar Equations 200
Step 4 Convert Equations Between Polar and Rectangular Forms 205
Step 5 Convert Equations Between Parametric and Function Forms 207
Step 6 Graph Parametric Equations 208
14 Transformations 211
Step 1 Understand the Geometry of Reflections 211
Step 2 Translate by Reflecting 217
Step 3 Rotate by Reflecting 221
Step 4 Dilate Geometrically 225
Step 5 Use Matrices for Transformations 233
15 Rotating Conics 240
Step 1 Create the Equation that Rotates a Conic 240
Step 2 Recognize Rotation in Equations 247
Step 3 Graph a Rotated Conic 248
Step 4 Classify Rotated Conics without Graphing 250
16 Complex Numbers 253
Step 1 Change Between Forms 253
Step 2 Add and Subtract Complex Numbers 257
Step 3 Multiply and Divide Complex Numbers 258
Step 4 Raise a Complex Number to a Power 261
Step 5 Find the Roots of a Complex Number 262
17 Limits 265
Step 1 Evaluate Limits 266
Step 2 Deal with Problems 271
Step 3 Use Properties of Limits 274
Step 4 Evaluate Infinite Limits and Limits at Infinity 275
18 Sequences and Series 278
Step 1 Find Terms of Sequences 278
Step 2 Find Limits of Sequences 280
Step 3 Find Sums of Series 281
Step 4 Find Sums of Infinite Series 283
Answer Key 285
Index 383