Pre-Calculus for Dummies - Mary Jane Sterling

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Résumé :

Introduction 1

About This Book 1

Foolish Assumptions 2

Icons Used in This Book 3

Beyond the Book 3

Where to Go from Here 3

Part 1: Getting Started with Pre-Calculus 5

Chapter 1: Pre-Pre-Calculus 7

Pre-Calculus: An Overview 8

All the Number Basics (No, Not How to Count Them!) 9

The multitude of number types: Terms to know 9

The fundamental operations you can perform on numbers 11

The properties of numbers: Truths to remember 11

Visual Statements: When Math Follows Form with Function 12

Basic terms and concepts 13

Graphing linear equalities and inequalities 14

Gathering information from graphs 15

Get Yourself a Graphing Calculator 16

Chapter 2: Playing with Real Numbers 19

Solving Inequalities 19

Recapping inequality how-tos 20

Solving equations and inequalities when absolute value is involved 20

Expressing solutions for inequalities with interval notation 22

Variations on Dividing and Multiplying: Working with Radicals and Exponents 24

Defining and relating radicals and exponents 24

Rewriting radicals as exponents (or, creating rational exponents) 25

Getting a radical out of a denominator: Rationalizing 26

Chapter 3: The Building Blocks of Pre-Calculus Functions 31

Qualities of Special Function Types and Their Graphs 32

Even and odd functions 32

One-to-one functions 32

Dealing with Parent Functions and Their Graphs 33

Linear functions 33

Quadratic functions 33

Square-root functions 34

Absolute-value functions 34

Cubic functions 35

Cube-root functions 36

Graphing Functions That Have More Than One Rule: Piece-Wise Functions 37

Setting the Stage for Rational Functions 38

Step 1: Search for vertical asymptotes 39

Step 2: Look for horizontal asymptotes 40

Step 3: Seek out oblique asymptotes 41

Step 4: Locate the x- and y-intercepts 42

Putting the Results to Work: Graphing Rational Functions 42

Chapter 4: Operating on Functions 49

Transforming the Parent Graphs 50

Stretching and flattening 50

Translations 52

Reflections 54

Combining various transformations (a transformation in itself!) 55

Transforming functions point by point 57

Sharpen Your Scalpel: Operating on Functions 58

Adding and subtracting 59

Multiplying and dividing 60

Breaking down a composition of functions 60

Adjusting the domain and range of combined functions (if applicable) 61

Turning Inside Out with Inverse Functions 63

Graphing an inverse 64

Inverting a function to find its inverse 66

Verifying an inverse 66

Chapter 5: Digging Out and Using Roots to Graph Polynomial Functions 69

Understanding Degrees and Roots 70

Factoring a Polynomial Expression 71

Always the first step: Looking for a GCF 72

Unwrapping the box containing a trinomial 73

Recognizing and factoring special polynomials 74

Grouping to factor four or more terms 77

Finding the Roots of a Factored Equation 78

Cracking a Quadratic Equation When It Won't Factor 79

Using the quadratic formula 79

Completing the square 80

Solving Unfactorable Polynomials with a Degree Higher Than Two 81

Counting a polynomial's total roots 82

Tallying the real roots: Descartes's rule of signs 82

Accounting for imaginary roots: The fundamental theorem of algebra 83

Guessing and checking the real roots 84

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Get ahead in pre-calculus

Pre-calculus courses have become increasingly popular with 35 percent of students in the U.S.?taking the course in middle or high school. Often, completion of such a course is a prerequisite for calculus and other upper level mathematics courses.

Pre-Calculus For Dummies is an invaluable resource for students enrolled in pre-calculus courses. By presenting the essential topics in a clear and concise manner, the book helps students improve their understanding of pre-calculus and become prepared for upper level math courses.

• Provides fundamental information in an approachable manner
• Includes fresh example problems
• Practical explanations mirror today's teaching methods
• Offers relevant cultural references

Whether used as a classroom aid or as a refresher in preparation for an introductory calculus course, this book is one you'll want to have on hand to perform your very best.