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## Overview

**Get the knowledge and skills you need to solve pre-calculus problems with confidence!**

The quickest route to learning a subject is through a solid grounding in the basics. Rather than endless drills, this accessible guide presents an original, step-by-step approach to help you develop a better understanding of pre-calculus topics. You’ll find important concepts linked together by clear explanations, invaluable exercises, and helpful worked-out problems. Once you’ve mastered the topics in this book, you will find yourself well-equipped to begin your calculus studies.

This book features:

• A new Trigonometry chapter that will round out your pre-calculus studies

• Clear explanations that break down concepts into easy-to-understand steps

• Stay-in-step "pop-ups" offering helpful advice and cautions against common errors

• Step-it-up skill-building exercises linking practice to the core steps already presented

• Worked-out solutions to all exercises that reinforce understanding of concepts

## Product Details

ISBN-13: | 9781260135114 |
---|---|

Publisher: | McGraw-Hill Professional Publishing |

Publication date: | 12/26/2018 |

Pages: | 400 |

Sales rank: | 139,447 |

Product dimensions: | 7.20(w) x 9.00(h) x 0.90(d) |

## About the Author

**Carolyn Wheater**taught math and computer technology for more than 40 years to students from elementary school through college. She continues to write about mathematics and test preparation and is a member of the National Council of Teachers of Mathematics.

## 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