1 of MATHEMATICS RELATIONS, FUNCTIONS, AND GRAPHS TABLE OF CONTENTS TELECOMMUNICATION Introduction, 3 Projects, 61, 123, 201, 271 Matrices, 97 Unit 1 Projects UNIT 1 Chapter 1 LINEAR RELATIONS AND FUNCTIONS 4 1-1 Relations and Functions ..............................................5 1-2 Composition of Functions .......................................13 1-3 Graphing Linear Equations ...................................20 1-3B Graphing Calculator Exploration Analyzing Families of Linear Graphs ...................26 1-4 Writing Linear Equations ........................................27 Mid-Chapter Quiz ..............................................................31 1-5 Writing Equations of Parallel and Perpendicular Lines ............................................32 1-6 Modeling Real-World Data with Linear Functions .....................................................................38 1-7 Piecewise Functions ..................................................45 1-8 Graphing Linear Inequalities ................................52 Study Guide and Assessment .......................................57 SAT & ACT Preparation ................................................62 Chapter 2 SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES 66 2-1 Solving Systems of Equations in Two Variables............................................................ 67 2-2 Solving Systems of Equations in Three Variables......................................................... 73 2-3 Modeling Real-World Data with Matrices ........... 78 2-4A Graphing Calculator Exploration Transformation Matrices.......................................................................87 2-4 Modeling Motion with Matrices .......................... 88 Mid-Chapter Quiz .........................................................96 2-5 Determinants and Multiplicative Inverses of Matrices................................................................. 98 2-5B Graphing Calculator Exploration Augmented Matrices and Reduced Row-Echelon Form ........106 2-6 Solving Systems of Linear Inequalities ................. 107 2-7 Linear Programming ............................................... 112 Study Guide and Assessment ......................................119 SAT & ACT Preparation...............................................124 vi
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1-1 Relations and Functions ..............................................51-2 Composition of Functions .......................................131-3 Graphing Linear Equations ...................................20
1-3B Graphing Calculator ExplorationAnalyzing Families of Linear Graphs...................26
1-4 Writing Linear Equations ........................................27
Formulas and Symbols ......................................inside back cover
CALCULUS
Unit 5 Project
DISEASESIntroduction, 940Project, 981
UNIT
5
GRAPHINGCALCULATOREXPLORATIONS
CAREER CHOICES
of
MATHEMATICS
Mathematician, 976
Calculus, 969
945, 949
xiv
#
USING A GRAPHING CALCULATOR
In Glencoe Advanced Mathematical Concepts, the graphing calculator is animportant tool in exploring precalculus topics. A graphing calculator is actuallya specialized hand-held computer. Graphing Calculator Explorations throughoutthis text offer opportunties for you to use a graphing calculator to explore themathematical topics you are studying. You will also see graphing calculatorscreens actually generated by a graphing calculator. If you do not recognize thekeys, commands, or screens shown in this test, you may have a different modelof calculator. Refer to your owner’s manual to verify the proper commands andkeystrokes to use.
Graphing Calculator Appendix
At the back of this text, you will find a Student Handbook. The GraphingCalculator Appendix begins on page A2. This appendix introduces you to someof the common functions of the graphing calculator most widely used in highschool classrooms. It is divided into nine sections:
1 Introduction to the Graphing Calculator
2 Graphing Functions
3 Analyzing Functions
4 Graphing Inequalities
5 Matrices
6 Graphing Trigonometric Functions
7 Graphing Special Functions
8 Parametric and Polar Equations
9 Statistics and Statistical Graphs
In each section, you will find keystrokeinstructions for specific examples thatdemonstrate some of the basic operationsand most common menus available on the calculator. Whenever you have specificquestions about commands or procedures,you should refer to your owner’s manual forinstruction.
SAT and ACT Preparation
It is important to note that graphingcalculators are permitted when taking theACT or SAT and are required for the APCalculus test. Through your experienceswith the graphing calculator in studyingGlencoe Advanced MathematicalConcepts, you should becomecomfortable with its operation andappreciate the power of this tinycomputer.
These sections donot correspondwith the order oftopics in thistextbook.
To findkeystrokeinstructions foreach GraphingCalculatorExploration, visitwww.amc.glencoe.com