Exponential Functions. Exponential Functions and Their Graphs.
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Transcript of 1 RELATIONS, FUNCTIONS, AND GRAPHS - Liberty High · PDF fileRELATIONS, FUNCTIONS, AND GRAPHS...
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MATHEMATICS
RELATIONS, FUNCTIONS, AND GRAPHS
TABLE OF CONTENTS
TELECOMMUNICATIONIntroduction, 3Projects, 61, 123, 201, 271
Matrices, 97
Unit 1 Projects
UNIT
1Chapter 1 LINEAR RELATIONS AND
FUNCTIONS 4
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
Mid-Chapter Quiz ..............................................................31
1-5 Writing Equations of Parallel andPerpendicular Lines ............................................32
1-6 Modeling Real-World Data with LinearFunctions .....................................................................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 EQUATIONSAND 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 TransformationMatrices.......................................................................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 ......................................119SAT & ACT Preparation...............................................124
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GRAPHINGCALCULATOREXPLORATIONS
UNIT 1
Veterinary Medicine, 12Agricultural Manager, 105Biomedical Engineering, 136Environmental Engineering,
221
Self-Check Quizzes, 9, 17,23, 29, 36, 42, 49, 55, 70,76, 83, 93, 102, 110, 116,134, 142, 149, 156, 165,176, 186, 194, 210, 219,226, 240, 247, 255, 262
Data Updates, 84, 263 Career Choices, 12, 105,
136, 221Internet Projects, 61, 123,
201, 271History of Mathematics, 97Graphing Calculator
Programs, 10, 133, 226Review Activities, 57, 119,
197, 267SAT/ACT Practice, 65, 125,
203, 273Chapter Tests, A56–A59
13, 26, 69, 86, 87, 106, 133,169, 232, 265
CAREER CHOICESChapter 3 THE NATURE OF GRAPHS 126
3-1 Symmetry and Coordinate Graphs.........................127
3-2 Families of Graphs.......................................................137
3-3 Graphs of Nonlinear Inequalities............................146
Mid-Chapter Quiz............................................................151
3-4 Inverse Functions and Relations...........................152
3-5 Continuity and End Behavior...................................159
3-5B Graphing Calculator Exploration Gap Discontinuities...........................................................169
3-6 Critical Points and Extrema....................................171
3-7 Graphs of Rational Functions............................... 180
3-8 Direct, Inverse, and Joint Variation ......................189
Study Guide and Assessment .......................................197
SAT & ACT Preparation..............................................202
Chapter 4 POLYNOMIAL AND RATIONALFUNCTIONS 204
4-1 Polynomial Functions............................................205
4-2 Quadratic Equations...............................................213
4-3 The Remainder and Factor Theorems..................222
4-4 The Rational Root Theorem ................................229
Mid-Chapter Quiz.......................................................235
4-5 Locating Zeros of a Polynomial Function ...........236
4-6 Rational Equations and Partial Fractions ............243
4-7 Radical Equations and Inequalities........................251
4-8 Modeling Real-World Data with Polynomial Functions.................................258
4-8B Graphing Calculator Exploration Fitting aPolynomial Function to a Set of Points .............265
Study Guide and Assessment.......................................267
SAT & ACT Preparation..............................................272
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TRIGONOMETRY
Unit 2 Projects
THE CYBERCLASSROOMIntroduction, 275Projects, 339, 417, 481, 547
UNIT
2
of
MATHEMATICS
Angles, 319Functions, 367Trigonometry, 462Angle Measure, 534
Chapter 5 THE TRIGONOMETRICFUNCTIONS 276
5-1 Angles and Degree Measure..................................277
5-2 Trigonometric Ratios in Right Triangles.............284
5-3 Trigonometric Functions on the Unit Circle........291
5-4 Applying Trigonometric Functions......................299
Mid-Chapter Quiz.......................................................304
5-5 Solving Right Triangles..........................................305
5-6 The Law of Sines.........................................................313
5-7 The Ambiguous Case for the Law of Sines..........320
5-8 The Law of Cosines ................................................327
5-8B Graphing Calculator ExplorationSolving Triangles..................................................333
Study Guide and Assessment.......................................335
SAT & ACT Preparation ..............................................340
Chapter 6 GRAPHS OF TRIGONOMETRICFUNCTIONS 342
6-1 Angles and Radian Measure..................................343
6-2 Linear and Angular Velocity....................................352
6-3 Graphing Sine and Cosine Functions...................359
6-4 Amplitude and Period of Sine and Cosine Functions ...................................................368
Mid-Chapter Quiz .......................................................377
6-5 Translations of Sine and Cosine Functions....................................................378
6-6 Modeling Real-World Data with SinusoidalFunctions....................................................................387
6-7 Graphing Other Trigonometric Functions...........395
6-7B Graphing Calculator ExplorationSound Beats ..........................................................404
6-8 Trigonometric Inverses and Their Graphs ..........405
Study Guide and Assessment........................................413
SAT & ACT Preparation...............................................418
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UNIT 2
CAREER CHOICES
Architecture, 312Audio Recording
Engineer, 358Cartographer, 430Aerospace Engineer, 499
Self-Check Quizzes, 281,288, 296, 302, 309, 316,329, 331, 348, 355, 363,373, 383, 396, 400, 410,427, 434, 442, 453, 459,467, 474, 490, 497, 503,509, 517, 524, 531, 540
Data Updates, 283, 455Research, 357, 388Career Choices, 312, 358,
430, 499Internet Projects, 339, 417,
481, 547History of Mathematics, 319,
367, 462, 534Graphing Calculator
Programs, 331, 333, 470, 512
Review Activities, 335, 413,477, 543
SAT/ACT Practice, 341, 419,483, 549
Chapter Tests, A60–A63
GRAPHINGCALCULATOREXPLORATIONS
284, 323, 333, 369, 378, 404,433, 446, 458, 512, 526
Chapter 7 TRIGONOMETRIC IDENTITIES AND EQUATIONS 420
7-1 Basic Trigonometric Identities..............................421
7-2 Verifying Trigonometric Identities........................431
7-3 Sum and Difference Identities...............................437
Mid-Chapter Quiz.......................................................445
7-3B Graphing Calculator ExplorationReduction Identities...........................................446
7-4 Double-Angle and Half-Angle Identities...............448
7-5 Solving Trigonometric Equations.........................456
7-6 Normal Form of a Linear Equation.......................463
7-7 Distance From a Point to a Line..............................470
Study Guide and Assessment.....................................477
SAT & ACT Preparation..............................................482
Chapter 8 VECTORS AND PARAMETRICEQUATIONS 484
8-1 Geometric Vectors......................................................485
8-2 Algebraic Vectors .................................................493
8-3 Vectors in Three-Dimensional Space ..................500
8-4 Perpendicular Vectors...........................................505
Mid-Chapter Quiz .......................................................5 1 1
8-4B Graphing Calculator ExplorationFinding Cross Products.......................................512
8-5 Applications with Vectors.....................................513
8-6 Vectors and Parametric Equations........................520
8-6B Graphing Calculator Exploration Modeling with Parametric Equations....................................526
8-7 Modeling Motion Using Parametric Equations..................................................................527
8-8 Transformational Matrices in Three-Dimensional Space ...................................535
Study Guide and Assessment.......................................543
SAT & ACT Preparation..............................................548
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Chapter 9 POLAR COORDINATES AND COMPLEX NUMBERS 552
9-1 Polar Coordinates.......................................................553
9-2 Graphs of Polar Equations.....................................561
9-3 Polar and Rectangular Coordinates.....................568
9-4 Polar Form of a Linear Equation.............................574
Mid-Chapter Quiz.......................................................579
9-5 Simplifying Complex Numbers...............................580
9-6 The Complex Plane and Polar Form of Complex Numbers ..................................................586
9-6B Graphing Calculator ExplorationGeometry in the Complex Plane..........................592
9-7 Products and Quotients of Complex Numbers in Polar Form........................593
9-8 Powers and Roots of Complex Numbers..............599
Study Guide and Assessment.....................................607
SAT & ACT Preparation...............................................612
Chapter 10 CONICS 614
10-1 Introduction to Analytic Geometry........................615
10-2 Circles......................................................................623
10-3 Ellipses..........................................................................631
10-4 Hyperbolas..............................................................642
10-5 Parabolas......................................................................653
Mid-Chapter Quiz ...........................................................661
10-6 Rectangular and Parametric Forms of Conic Sections ....................................................662
10-7 Transformations of Conics....................................670
10-8 Systems of Second-Degree Equations andInequalities ...............................................................678
10-8B Graphing Calculator ExplorationShading Areas on a Graph .................................685
Study Guide and Assessment.......................................687
SAT & ACT Preparation..............................................692
ADVANCED FUNCTIONS AND GRAPHING
Unit 3 Projects
SPACE—THE FINALFRONTIER
Introduction, 551Projects, 611, 691, 753
UNIT
3
x
Chapter 11 EXPONENTIAL AND LOGARITHMICFUNCTIONS 694
11-1 Real Exponents.......................................................695
11-2 Exponential Functions..............................................704
11-3 The Number e ..........................................................712
Mid-Chapter Quiz........................................................717
11-4 Logarithmic Functions ..............................................718
11-5 Common Logarithms................................................726
11-6 Natural Logarithms ...................................................733
11-6B Graphing Calculator ExplorationNatural Logarithms and Area .............................738
11-7 Modeling Real-World Data with Exponential and Logarithmic Functions...................................740
Study Guide and Assessment.....................................749
SAT & ACT Preparation ..............................................754
GRAPHINGCALCULATOREXPLORATIONS
CAREER CHOICES
Astronomer, 598Meteorologist, 622Food Technologist, 703
592, 602, 641, 665, 685, 695,705, 738
UNIT 3
Self-Check Quizzes, 558,565, 571, 578, 583, 590,596, 605, 620, 627, 638,650, 659, 667, 675, 682,700, 708, 714, 720, 723,730, 735, 744
Data Updates, 741 Career Choices, 598, 622,
703Internet Projects, 611, 691,
753Graphing Calculator
Programs, 582, 604, 620,628, 710
Review Activities, 607, 687,749
SAT/ACT Practice, 613, 693,755
Chapter Tests, A64–A66
Lesson 10-7, page 675
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Self-Check Quizzes, 763,771, 781, 791, 798, 804,812, 819, 826, 843, 849,856, 864, 871, 878, 893,903, 914, 923, 930
Data Updates, 895, 906, 908Career Choices, 800, 851,
896Internet Projects, 833, 885,
937Graphing Calculator
Programs, 784Review Activities, 829, 881,
933SAT/ACT Practice, 835, 887,
939 Chapter Tests, A67–A69
Chapter 12 SEQUENCES AND SERIES 758
12-1 Arithmetic Sequences and Series.........................759
12-2 Geometric Sequences and Series .........................766
12-3 Infinite Sequences and Series .................................774
12-3B Graphing Calculator ExplorationContinued Fractions...............................................784
12-4 Convergent and Divergent Series.........................786
Mid-Chapter Quiz.......................................................793
12-5 Sigma Notation and the nth Term ........................794
12-6 The Binomial Theorem...........................................801
12-7 Special Sequences and Series...............................806
12-8 Sequences and Iteration ........................................815
12-9 Mathematical Induction ........................................822
Study Guide and Assessment.......................................829
SAT & ACT Preparation..............................................834
Chapter 13 COMBINATORICS AND PROBABILITY 836
13-1 Permutations and Combinations...........................837
13-2 Permutations with Repetitions and Circular Permutations.........................................846
13-3 Probability and Odds...........................................852
Mid-Chapter Quiz..........................................................858
13-4 Probabilities of Compound Events .....................859
13-5 Conditional Probability............................................868
13-6 The Binomial Theorem and Probability ..............875
Study Guide and Assessment ........................................881
SAT & ACT Preparation..............................................886
DISCRETE MATHEMATICS
Unit 4 Projects
THE UNITED STATESCENSUS BUREAU
Introduction, 757Projects, 833, 885, 937
UNIT
4
CAREER CHOICES
Operation Research Analyst,800
Actuary, 851Accountant, 896
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Chapter 14 STATISTICS AND DATA ANALYSIS 888
14-1 The Frequency Distribution....................................889
14-2 Measures of Central Tendency.............................897
14-3 Measures of Variability..........................................908
Mid-Chapter Quiz........................................................917
14-4 The Normal Distribution........................................918
14-4B Graphing Calculator ExplorationThe Standard Normal Curve ................................926
14-5 Sample Sets of Data................................................927
Study Guide and Assessment.......................................933
SAT & ACT Preparation..............................................938
GRAPHINGCALCULATOREXPLORATIONS
784, 809, 877, 926
UNIT 4
Lesson 12-5, page 798
xiii
Self-Check Quizzes, 946,958, 966, 973
Data Updates, 956Research, 943, 970 Career Choices, 976Internet Project, 981History of Mathematics, 969Graphing Calculator
Programs, 961Review Activities, 977SAT/ACT Practice, 983Chapter Test, A70
Chapter 15 INTRODUCTION TO CALCULUS 940
15-1 Limits ........................................................................941
15-2A Graphing Calculator ExplorationThe Slope of a Curve ..............................................949
15-2 Derivatives and Antiderivatives............................951
Mid-Chapter Quiz.......................................................960
15-3 Area Under a Curve...............................................961
15-4 The Fundamental Theorem of Calculus..............970
Study Guide and Assessment.....................................977
SAT & ACT Preparation..............................................982
Student Handbook
Graphing Calculator Appendix.....................................................A2
Extra Practice....................................................................................A26
Chapter Tests ...............................................................................A56
Glossary .........................................................................................A71
Selected Answers..........................................................................A81
Photo Credits ..............................................................................A152
Index.............................................................................................A154
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
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#
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
Using a Graphing Calculator 1