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.
Autorentext
Mary Jane Sterling aught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.
Klappentext
- Make sense of logarithms and exponentials
- Understand functions and solve linear equations
- Graph algebraic and trig functions
Get ahead in pre-calculus
Getting a handle on pre-calculus can feel a bit daunting, but this accessible, hands-on guide makes it easier than ever. By presenting the essential topics in a clear and concise manner, the book helps you improve your understanding of pre-calculus and become prepared for upper-level math coursesin a snap!
Inside...
- Sharpen your algebraic skills
- Identify and conquer challenging processes
- Review angles and their properties
- Establish trig identities
- Work with conic sections
- Solve systems of equations
Zusammenfassung
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.
Inhalt
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
Put It in Reverse: Using Solutions to Find Factors 90
Graphing Polynomials 91