Easy Pre-Calculus Step-by-Step, Second Edition

by Carolyn Wheater

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 LLC
Publication date:	12/26/2018
Pages:	400
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