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Precalculus: Graphs & Models [Hardback]

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  • Formāts: Hardback, 2912 pages, height x width x depth: 282x224x51 mm, weight: 3105 g, 3620 Illustrations
  • Izdošanas datums: 16-Apr-2011
  • Izdevniecība: McGraw Hill Higher Education
  • ISBN-10: 0073519537
  • ISBN-13: 9780073519531
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Precalculus: Graphs & ModelsPalielināt
  • Formāts: Hardback, 2912 pages, height x width x depth: 282x224x51 mm, weight: 3105 g, 3620 Illustrations
  • Izdošanas datums: 16-Apr-2011
  • Izdevniecība: McGraw Hill Higher Education
  • ISBN-10: 0073519537
  • ISBN-13: 9780073519531
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780073519531.html
Keywords:
Three components contribute to a theme sustained throughout the Coburn/Herdlick Graphs and Models series: that of laying a firm foundation, building a solid framework, and providing strong connections. In the Graphs and Models texts, the authors combine their depth of experience with the conversational style and the wealth of applications that the Coburn/Herdlick texts have become known for. By combining a graphical approach to problem solving with algebraic methods, students learn how to relate their mathematical knowledge to the outside world. The authors use technology to solve the more true to life equations, to engage more applications, and to explore the more substantial questions involving graphical behavior. Benefiting from the feedback of hundreds of instructors and students across the country, Precalculus: Graphs & Models emphasizes connections in order to improve the level of student engagement in mathematics and increase their chances of success in precalculus and calculus.

The launch of the Coburn/Herdlick Graphs and Models series provides a significant leap forward in terms of online course management with McGraw-Hill’s new homework platform, Connect Math Hosted by ALEKS Corp. Math instructors served as digital contributors to choose the problems that will be available, authoring each algorithm and providing stepped out solutions that go into great detail and are focused on areas where students commonly make mistakes. From there, the ALEKS Corporation reviewed each algorithm to ensure accuracy. A unifying theme throughout the entire process was the involvement of the authors. Through each step, they provided feedback and guidance to the digital contributors to ensure that the content being developed digitally closely matched the textbook. The result is an online homework platform that provides superior content and feedback, allowing students to effectively learn the material being taught.
Preface vi
Index of Applications xxxv
Chapter 1 Relations, Functions, and Graphs 1(104)
1.1 Rectangular Coordinates; Graphing Circles and Other Relations
2(17)
1.2 Linear Equations and Rates of Change
19(14)
1.3 Functions, Function Notation, and the Graph of a Function
33(17)
Mid-Chapter Check
48(1)
Reinforcing Basic Concepts: Finding the Domain and Range of a Relation from Its Graph
48(2)
1.4 Linear Functions, Special Forms, and More on Rates of Change
50(14)
1.5 Solving Equations and Inequalities Graphically; Formulas and Problem Solving
64(15)
1.6 Linear Function Models and Real Data
79(26)
Making Connections
93(1)
Summary and Concept Review
94(5)
Practice Test
99(1)
Strengthening Core Skills: The Various Forms of a Linear Equation
100(1)
Calculator Exploration and Discovery: Evaluating Expressions and Looking for Patterns
101(2)
Connections to Calculus: Tangent Lines
103(2)
Chapter 2 More on Functions 105(98)
2.1 Analyzing the Graph of a Function
106(14)
2.2 The Toolbox Functions and Transformations
120(16)
2.3 Absolute Value Functions, Equations, and Inequalities
136(12)
Mid-Chapter Check
146(1)
Reinforcing Basic Concepts: Using Distance to Understand Absolute Value Equations and Inequalities
147(1)
2.4 Basic Rational Functions and Power Functions; More on the Domain
148(15)
2.5 Piecewise-Defined Functions
163(14)
2.6 Variation: The Toolbox Functions in Action
177(26)
Making Connections
188(1)
Summary and Concept Review
189(4)
Practice Test
193(2)
Calculator Exploration and Discovery: Studying Joint Variations
195(1)
Strengthening Core Skills: Variation and Power Functions: y = kxP
196(1)
Cumulative Review:
Chapters 1-2
197(2)
Connections to Calculus: Solving Various Types of Equations; Absolute Value Inequalities and Delta/Epsilon Form
199(4)
Chapter 3 Quadratic Functions and Operations on Functions 203(104)
3.1 Complex Numbers
204(10)
3.2 Solving Quadratic Equations and Inequalities
214(21)
3.3 Quadratic Functions and Applications
235(15)
Mid-Chapter Check
249(1)
Reinforcing Basic Concepts: An Alternative Method for Checking Solutions to Quadratic Equations
249(1)
3.4 Quadratic Models; More on Rates of Change
250(12)
3.5 The Algebra of Functions
262(12)
3.6 The Composition of Functions and the Difference Quotient
274(33)
Making Connections 292 Summary and Concept Review 292 Practice Test
297(1)
Calculator Exploration and Discovery: Residuals, Correlation Coefficients, and Goodness of Fit
298(2)
Strengthening Core Skills: Base Functions and Quadratic Graphs
300(1)
Cumulative Review:
Chapters 1-3
301(2)
Connections to Calculus: Rates of Change and the Difference Quotient; Transformations and the Area Under a Curve
303(4)
Chapter 4 Polynomial and Rational Functions 307(102)
4.1 Synthetic Division; the Remainder and Factor Theorems
308(12)
4.2 The Zeroes of Polynomial Functions
320(17)
4.3 Graphing Polynomial Functions
337(19)
Mid-Chapter Check
354(1)
Reinforcing Basic Concepts: Approximating Real Zeroes
355(1)
4.4 Graphing Rational Functions
356(15)
4.5 Additional Insights into Rational Functions
371(14)
4.6 Polynomial and Rational Inequalities
385(24)
Making Connections
396(1)
Summary and Concept Review
396(4)
Practice Test
400(1)
Calculator Exploration and Discovery: Complex Zeroes, Repeated Zeroes, and Inequalities
401(1)
Strengthening Core Skills: Solving Inequalities Using the Push Principle
402(1)
Cumulative Review:
Chapters 1-4
403(2)
Connections to Calculus: Graphing Techniques
405(4)
Chapter 5 Exponential and Logarithmic Functions 409(100)
5.1 One-to-One and Inverse Functions
410(12)
5.2 Exponential Functions
422(11)
5.3 Logarithms and Logarithmic Functions
433(13)
5.4 Properties of Logarithms
446(11)
Mid-Chapter Check
456(1)
Reinforcing Basic Concepts: Understanding Properties of Logarithms
457(1)
5.5 Solving Exponential and Logarithmic Equations
457(12)
5.6 Applications from Business, Finance, and Science
469(13)
5.7 Exponential, Logarithmic, and Logistic Equation Models
482(27)
Making Connections
495(1)
Summary and Concept Review
496(5)
Practice Test
501(1)
Calculator Exploration and Discovery: Investigating Logistic Equations
502(1)
Strengthening Core Skills: The HerdBurn Scale-What's Hot and What's Not
503(1)
Cumulative Review:
Chapters 1-5
504(1)
Connections to Calculus: Properties of Logarithms; Area Functions; Expressions Involving ex
505(4)
Chapter 6 An Introduction to Trigonometric Functions 509(144)
6.1 Angle Measure, Special Triangles, and Special Angles
510(17)
6.2 Unit Circles and the Trigonometry of Real Numbers
527(15)
6.3 Graphs of the Sine and Cosine Functions
542(19)
6.4 Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions
561(17)
Mid-Chapter Check
577(1)
Reinforcing Basic Concepts: Trigonometry of the Real Numbers and the Wrapping Function
577(1)
6.5 Transformations and Applications of Trigonometric Graphs
578(17)
6.6 The Trigonometry of Right Triangles
595(15)
6.7 Trigonometry and the Coordinate Plane
610(12)
6.8 Trigonometric Equation Models
622(31)
Making Connections
633(1)
Summary and Concept Review
634(9)
Practice Test
643(2)
Calculator Exploration and Discovery: Variable Amplitudes and Modeling the Tides
645(1)
Strengthening Core Skills: Standard Angles, Reference Angles, and the Trig Functions
646(2)
Cumulative Review:
Chapters 1-6
648(2)
Connections to Calculus: Right Triangle Relationships; Converting from Rectangular Coordinates to Trigonometric (Polar) Form
650(3)
Chapter 7 Trigonometric Identities, Inverses, and Equations 653(92)
7.1 Fundamental Identities and Families of Identities
654(7)
7.2 More on Verifying Identities
661(8)
7.3 The Sum and Difference Identities
669(11)
7.4 The Double-Angle, Half-Angle and Product-to-Sum Identities
680(15)
Mid-Chapter Check
693(1)
Reinforcing Basic Concepts: Identities-Connections and Relationships
693(2)
7.5 The Inverse Trig Functions and Their Applications
695(16)
7.6 Solving Basic Trig Equations
711(10)
7.7 General Trig Equations and Applications
721(24)
Making Connections
732(1)
Summary and Concept Review
733(4)
Practice Test
737(2)
Calculator Exploration and Discovery: Seeing the Beats as the Beats Go On
739(1)
Strengthening Core Skills: Trigonometric Equations and Inequalities
739(2)
Cumulative Review:
Chapters 1-7
741(2)
Connections to Calculus: Simplifying Expressions Using a Trigonometric Substitution; Trigonometric Identities and Equations
743(2)
Chapter 8 Applications of Trigonometry 745(92)
8.1 Oblique Triangles and the Law of Sines
746(13)
8.2 The Law of Cosines; the Area of a Triangle
759(12)
8.3 Vectors and Vector Diagrams
771(16)
Mid-Chapter Check
786(1)
Reinforcing Basic Concepts: Scaled Drawings and the Laws of Sine and Cosine
786(1)
8.4 Vectors Applications and the Dot Product
787(15)
8.5 Complex Numbers in Trigonometric Form
802(11)
8.6 De Moivre's Theorem and the Theorem on nth Roots
813(24)
Making Connections
821(1)
Summary and Concept Review
822(4)
Practice Test
826(2)
Calculator Exploration and Discovery: Investigating Projectile Motion
828(1)
Strengthening Core Skills: Vectors and Static Equilibrium
828(1)
Cumulative Review:
Chapters 1-8
829(3)
Connections to Calculus: Trigonometry and Problem Solving; Vectors in Three Dimensions
832(5)
Chapter 9 Systems of Equations and Inequalities 837(124)
9.1 Linear Systems in Two Variables with Applications
838(15)
9.2 Linear Systems in Three Variables with Applications
853(12)
9.3 Systems of Inequalities and Linear Programming
865(14)
9.4 Partial Fraction Decomposition
879(14)
Mid-Chapter Check
891(1)
Reinforcing Basic Concepts: Window Size and Graphing Technology
892(1)
9.5 Solving Linear Systems Using Matrices and Row Operations
893(12)
9.6 The Algebra of Matrices
905(12)
9.7 Solving Linear Systems Using Matrix Equations
917(16)
9.8 Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More
933(28)
Making Connections
947(1)
Summary and Concept Review
948(5)
Practice Test
953(1)
Calculator Exploration and Discovery: Cramer's Rule
954(1)
Strengthening Core Skills: Augmented Matrices and Matrix Inverses
955(1)
Cumulative Review:
Chapters 1-9
956(2)
Connections to Calculus: More on Partial Fraction Decomposition; The Geometry of Vectors and Determinants
958(3)
Chapter 10 Analytical Geometry and the Conic Sections 961(116)
10.1 A Brief Introduction to Analytic Geometry
962(7)
10.2 The Circle and the Ellipse
969(15)
10.3 The Hyperbola
984(13)
10.4 The Analytic Parabola
997(10)
Mid-Chapter Check
1006(1)
Reinforcing Basic Concepts: More on Completing the Square
1006(1)
10.5 Nonlinear Systems of Equations and Inequalities
1007(11)
10.6 Polar Coordinates, Equations, and Graphs
1018(17)
10.7 More on the Conic Sections: Rotation of Axes and Polar Form
1035(16)
10.8 Parametric Equations and Graphs
1051(26)
Making Connections
1064(1)
Summary and Concept Review
1064(5)
Practice Test
1069(1)
Calculator Exploration and Discovery: Elongation and Eccentricity
1070(1)
Strengthening Core Skills: Ellipses and Hyperbolas with Rational/Irrational Values of a and b
1071(1)
Cumulative Review:
Chapters 1-10
1072(1)
Connections to Calculus: Polar Graphs and Instantaneous Rates of Change; Systems of Polar Equations
1073(4)
Chapter 11 Additional Topics in Algebra 1077(92)
11.1 Sequences and Series
1078(11)
11.2 Arithmetic Sequences
1089(9)
11.3 Geometric Sequences
1098(14)
11.4 Mathematical Induction
1112(8)
Mid-Chapter Check
1119(1)
Reinforcing Basic Concepts: Applications of Summation
1119(1)
11.5 Counting Techniques
1120(12)
11.6 Introduction to Probability
1132(13)
11.7 The Binomial Theorem
1145(24)
Making Connections
1153(1)
Summary and Concept Review
1154(4)
Practice Test
1158(2)
Calculator Exploration and Discovery: Infinite Series, Finite Results
1160(1)
Strengthening Core Skills: Probability, Quick-Counting, and Card Games
1161(1)
Cumulative Review:
Chapters 1-11
1162(3)
Connections to Calculus: Applications of Summation
1165(4)
Chapter 12 Bridges to Calculus: An Introduction to Limits 1169
12.1 An Introduction to Limits Using Tables and Graphs
1170(10)
12.2 The Properties of Limits
1180(11)
Mid-Chapter Check
1190(1)
12.3 Continuity and More on Limits
1191(12)
12.4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve
1203
Making Connections
1215(1)
Summary and Concept Review
1216(2)
Practice Test
1218(1)
Calculator Exploration and Discovery: Technology and the Area Under a Curve
1219(1)
Cumulative Review:
Chapters 1-12
1220
Appendix A A Review of Basic Concepts and Skills A-1
A.1 Algebraic Expressions and the Properties of Real Numbers
A-1
A.2 Exponents, Scientific Notation, and a Review of Polynomials
A-10
A.3 Solving Linear Equations and Inequalities
A-24
A.4 Factoring Polynomials and Solving Polynomial Equations by Factoring
A-38
A.5 Rational Expressions and Equations
A-52
A.6 Radicals, Rational Exponents, and Radical Equations
A-64
Overview of Appendix A
A-80
Practice Test
A-82
Appendix B Proof Positive-A Selection of Proofs from Precalculus A-84
Appendix C More on Synthetic Division A-89
Appendix D Reduced Row-Echelon Form and More on Matrices A-91
Appendix E The Equation of a Conic A-93
Appendix F Families of Polar Curves A-95
Student Answer Appendix (SE only) SA-1
Instructor Answer Appendix (AIE only) IA-1
Index I-1
John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelors Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Whos Who Among Americas Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one for all students.