Advanced Mathematical Concepts

by Gordon-Holliday, Berchie W.; Yunker, L. E.; Vannatta, Glen D.; Crosswhite, F. Joe

• ISBN13: 9780028242866
• ISBN10: 0028242866
• Format: Hardcover
• Copyright: 1997-01-01
• Publisher: Glencoe/McGraw-Hill School Pub Co

Table of Contents

Unit 1 Relations, Functions, and Graphs	2	(236)
Linear Relations and Functions	4	(48)
Relations and Functions	6	(6)
Case Study Follow-Up	11	(1)
Composition and Inverses of Functions	12	(9)
Graphing Calculators: Graphics Linear Equations and Inequalities	19	(2)
Linear Functions and Inequalities	21	(8)
Mid-Chapter Review	27	(1)
Technology: Graphing Linear Relations	28	(1)
Distance and Slope	29	(7)
Forms of Linear Equations	36	(6)
Parallel and Perpendicular Lines	42	(10)
Decision Making: Recycling	47	(1)
Chapter Summary and Review	48	(3)
Chapter Test	51	(1)
Systems of Equations and Inequalities	52	(50)
Graphing Calculators: Graphing Systems of Linear Equations	54	(2)
Solving Systems of Equations	56	(8)
Graphing Calculators: Matrices	62	(2)
Introduction to Matrices	64	(7)
Decision Making: Choosing a College Major	70	(1)
Determinants and Multiplicative Inverses of Matrices	71	(8)
Mid-Chapter Review	77	(1)
Technology: Finding Determinants of Matrices	78	(1)
Solving Systems of Equations by Using Matrices	79	(7)
Graphing Calculators: Graphing Systems of Linear Inequalities	84	(2)
Solving Systems of Inequalities	86	(5)
Linear Programming	91	(11)
Case Study Follow-Up	97	(1)
Chapter Summary and Review	98	(3)
Chapter Test	101	(1)
The Nature of Graphs	102	(74)
Graphing Calculators: Graphing Polynomial Functions	104	(2)
Symmetry	106	(11)
Decision Making: The Ozone Layer	116	(1)
Families of Graphs	117	(9)
Graphing Calculators: Graphing Radical Functions	125	(1)
Inverse Functions and Relations	126	(8)
Graphing Calculators: Graphing Rational Functions	132	(2)
Rational Functions and Asymptotes	134	(10)
Technology: Graphing Rational Functions	143	(1)
Graphs of Inequalities	144	(5)
Mid-Chapter Review	148	(1)
Tangent to a Curve	149	(7)
Graphing Calculators: Locating Critical Points of Polynomial Functions	155	(1)
Graphs and Critical Points of Polynomial Functions	156	(8)
Case Study Follow-Up	163	(1)
Continuity and End Behavior	164	(12)
Chapter Summary and Review	172	(3)
Chapter Test	175	(1)
Polynomial and Rational Functions	176	(60)
Polynomial Functions	178	(9)
Case Study Follow-Up	184	(1)
Graphing Calculators: Graphing Quadratic Functions	185	(2)
Quadratic Equations and Inequalities	187	(8)
Decision Making: Choosing a Vacation Spot	194	(1)
The Remainder and Factor Theorems	195	(6)
The Rational Root Theorem	201	(8)
Mid-Chapter Review	207	(1)
Graphing Calculators: Locating Zeros of Polynomial Functions	208	(1)
Locating the Zeros of a Function	209	(7)
Technology: Locating Zeros and Critical Points	215	(1)
Rational Equations and Partial Fractions	216	(9)
Graphing Calculators: Solving Radical Equations and Inequalities	223	(2)
Radical Equations and Inequalties	225	(11)
Chapter Summary and Review	230	(3)
Chapter Test	233	(1)
Unit 1 Review	234	(2)
Unit 2 Trigonometry	236	(226)
The Trigonometric Functions	238	(62)
Angles and Their Measure	240	(7)
Central Angles and Arcs	247	(8)
Decision Making: Education and Literacy	254	(1)
Circular Functions	255	(8)
Mid-Chapter Review	262	(1)
Trigonometric Functions of Special Angles	263	(6)
Right Triangles	269	(7)
Case Study Follow-Up	275	(1)
The Law of Sines	276	(7)
Technology: Solving Triangles	282	(1)
The Law of Cosines	283	(5)
Area of Triangles	288	(12)
Chapter Summary and Review	296	(3)
Chapter Test	299	(1)
Graphs and Inverses of the Trigonometric Functions	300	(56)
Graphs of the Trigonometric Functions	302	(7)
Decision Making: Drunk Driving	307	(1)
Technology: Ordered Pairs for Graphing Trigonometric Functions	308	(1)
Amplitude, Period, and Phase Shift	309	(12)
Case Study Follow-Up	318	(1)
Graphing Calculators: Graphing Trigonometric Functions	319	(2)
Graphing Trigonometric Functions	321	(7)
Inverse Trigonometric Functions	328	(6)
Mid-Chapter Review	333	(1)
Principal Values of the Inverse Trigonometric Functions	334	(6)
Graphing Calculators: Graphing Inverses of Trigonometric Functions	339	(1)
Graphing Inverses of Trigonometric Functions	340	(5)
Simple Harmonic Motion	345	(11)
Chapter Summary and Review	352	(3)
Chapter Test	355	(1)
Trigonometric Identities and Equations	356	(54)
Basic Trigonometric Identities	358	(6)
Verifying Trigonometric Identities	364	(7)
Graphing Calculators: Verifying Trigonometric Identities	369	(2)
Sum and Difference Identities	371	(6)
Double-Angle and Half-Angle Identities	377	(10)
Mid-Chapter Review	383	(1)
Technology: Double and Half Angles	384	(1)
Graphing Calculators: Solving Trigonometric Equations	385	(2)
Solving Trigonometric Equations	387	(5)
Case Study Follow-Up	391	(1)
Normal Form of a Linear Equation	392	(6)
Decision Making: Writing a Budget	397	(1)
Distance from a Point to a Line	398	(12)
Chapter Summary and Review	406	(3)
Chapter Test	409	(1)
Vectors and Parametric Equations	410	(52)
Geometric Vectors	412	(7)
Algebraic Vectors	419	(6)
Decision Making: Choosing a Used Car	424	(1)
Vectors in Three-Dimensional Space	425	(5)
Perpendicular Vectors	430	(6)
Mid-Chapter Review	435	(1)
Applications with Vectors	436	(6)
Case Study Follow-Up	441	(1)
Vectors and Parametric Equations	442	(7)
Technology: Using Parametric Equations	448	(1)
Using Parametric Equations to Model Motion	449	(13)
Chapter Summary and Review	456	(3)
Chapter Test	459	(1)
Unit 2 Review	460	(2)
Unit 3 Advanced Functions and Graphing	462	(190)
Polar Coordinates and Complex Numbers	464	(58)
Polar Coordinates	466	(9)
Decision Making: The Budget Deficit	472	(1)
Graphing Calculators: Graphing Polar Equations	473	(2)
Graphs of Polar Equations	475	(8)
Case Study Follow-Up	481	(1)
Technology: Graphing Polar Equations	482	(1)
Polar and Rectangular Coordinates	483	(5)
Polar Form of a Linear Function	488	(6)
Mid-Chapter Review	493	(1)
Simplifying Complex Numbers	494	(7)
Polar Form of Complex Numbers	501	(5)
Products and Quotients of Complex Numbers in Polar Form	506	(4)
Powers and Roots of Complex Numbers	510	(12)
Chapter Summary and Review	518	(3)
Chapter Test	521	(1)
Conics	522	(74)
The Circle	524	(10)
Decision Making: Choosing a Home Computer	532	(1)
Graphing Calculators: Locating the Vertex of a Parabola	533	(1)
The Parabola	534	(8)
The Ellipse	542	(9)
Case Study Follow-Up	550	(1)
The Hyperbola	551	(10)
Mid-Chapter Review	559	(1)
Technology: Asymptotes of a Hyperbola	560	(1)
Conic Sections	561	(9)
Graphing Calculators: Conic Sections	568	(2)
Transformations of Conics	570	(9)
Graphing Calculators: Solving Quadratic Systems	577	(2)
Systems of Second-Degree Equations and Inequalities	579	(6)
Tangents and Normals to the Conic Sections	585	(11)
Chapter Summary and Review	592	(3)
Chapter Test	595	(1)
Exponential and Logarithmic Functions	596	(56)
Rational Exponents	598	(8)
Decision Making: Homelessness	604	(1)
Graphing Calculators: Graphing Exponential Functions	605	(1)
Exponential Functions	605	(1)
Exponential Functions	606	(8)
The Number e	614	(8)
Case Study Follow-Up	619	(1)
Technology: Compound Interest	620	(1)
Graphing Calculators: Graphing Logarithmic Functions	621	(1)
Logarithmic Functions	621	(1)
Logarithmic Functions	622	(7)
Mid-Chapter Review	628	(1)
Common Logarithms	629	(7)
Graphing Calculators: Exponential and Logarithmic Equations and Inequalities	634	(2)
Exponential and Logarithmic Equations	636	(5)
Natural Logarithms	641	(11)
Chapter Summary and Review	646	(3)
Chapter Test	649	(1)
Unit 3 Review	650	(2)
Unit 4 Discrete Mathematics	652	(258)
Sequences and Series	654	(56)
Arithmetic Sequences and Series	656	(7)
Case Study Follow-Up	662	(1)
Geometric Sequences and Series	663	(8)
Technology: Amortization	670	(1)
Infinite Sequences and Series	671	(8)
Decision Making: Finding Money for College	678	(1)
Convergent and Divergent Series	679	(6)
Mid-Chapter Review	684	(1)
Sigma Notation and the nth Term	685	(6)
The Binomial Theorem	691	(5)
Special Sequences and Series	696	(6)
Mathematical Induction	702	(8)
Chapter Summary and Review	706	(3)
Chapter Test	709	(1)
Iteration and Fractals	710	(40)
Iterating Functions with Real Numbers	712	(5)
Graphical Iteration of Linear Functions	717	(5)
Graphical Iteration of the Logistic Function	722	(8)
Mid-Chapter Review	728	(1)
Technology: Graphical Iteration	729	(1)
Complex Numbers and Iteration	730	(4)
Decision Making: Crime	733	(1)
Escape Points, Prisoner Points, and Julia Sets	734	(6)
The Mandelbrot Set	740	(10)
Case Study Follow-Up	745	(1)
Chapter Summary and Review	746	(3)
Chapter Test	749	(1)
Combinatorics and Probability	750	(50)
Permutations	752	(6)
Decision Making: Choosing Car Insurance	757	(1)
Permutations with Repetitions and Circular Permutations	758	(6)
Combinations	764	(4)
Mid-Chapter Review	767	(1)
Probability and Odds	768	(6)
Case Study Follow-Up	773	(1)
Probabilities of Independent and Dependent Events	774	(5)
Probabilities of Mutually Exclusive or Inclusive Events	779	(5)
Conditional Probability	784	(6)
The Binomial Theorem and Probability	790	(10)
Technology: Dice Roll Simulation	795	(1)
Chapter Summary and Review	796	(3)
Chapter Test	799	(1)
Statistics and Data Analysis	800	(64)
The Frequency Distribution	802	(9)
Decision Making: Car Airbags	810	(1)
Measures of Central Tendency	811	(9)
Measures of Variability	820	(10)
Case Study Follow-Up	829	(1)
The Normal Distribution	830	(8)
Mid-Chapter Review	837	(1)
Sample Sets of Data	838	(8)
Graphing Calculators: Scatter Plots and Lines of Regression	844	(2)
Scatter Plots	846	(18)
Technology: Median-Fit Lines	855	(1)
Graphing Calculators: Curve Fitting	856	(4)
Chapter Summary and Review	860	(3)
Chapter Test	863	(1)
Graph Theory	864	(46)
Graphs	866	(6)
Walks and Paths	872	(5)
Euler Paths and Circuits	877	(6)
Mid-Chapter Review	882	(1)
Shortest Paths and Minimal Distances	883	(7)
Case Study Follow-Up	889	(1)
Trees	890	(6)
Decision Making: Planning a Party	895	(1)
Graphs and Matrices	896	(14)
Chapter Summary and Review	904	(3)
Chapter Test	907	(1)
Unit 4 Review	908	(2)
Unit 5 An Introduction to Calculus	910	(46)
Limits, Derivatives, and Integrals	912	(44)
Limits	914	(9)
Derivatives and Differentiation Techniques	923	(8)
Case Study Follow-Up	930	(1)
Area Under a Curve	931	(8)
Mid-Chapter Review	937	(1)
Technology: Riemann Sums	938	(1)
Integration	939	(6)
The Fundamental Theorem of Calculus	945	(11)
Decision Making: Planning a Move	951	(1)
Chapter Summary and Review	952	(3)
Chapter Test	955	(1)
Case Studies	956	(14)
Symbols	970	(1)
Formulas	971	(1)
Glossary	972	(7)
Selected Answers	979	(35)
Index	1014	(9)
Photo Credits	1023