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Precalculus: Graphs and Models 5th Revised edition [Hardback]

  • Formāts: Hardback, 1120 pages, height x width: 254x203 mm, weight: 1950 g
  • Izdošanas datums: 29-Jan-2012
  • Izdevniecība: Pearson
  • ISBN-10: 0321783964
  • ISBN-13: 9780321783967
Citas grāmatas par šo tēmu:
  • Formāts: Hardback, 1120 pages, height x width: 254x203 mm, weight: 1950 g
  • Izdošanas datums: 29-Jan-2012
  • Izdevniecība: Pearson
  • ISBN-10: 0321783964
  • ISBN-13: 9780321783967
Citas grāmatas par šo tēmu:

The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students “see the math” through its focus on visualization and technology. These texts continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications.

 

With the Fifth Edition, visualization is taken to a new level with technology. The authors also integrate smartphone apps, encouraging readers to visualize the math. In addition, ongoing review has been added with new Mid-Chapter Mixed Review exercise sets and new Study Guide summaries to help students prepare for tests.
Preface xi
To the Student xix
Interactive Figures Index xx
R Basic Concepts of Algebra
1(990)
R.1 The Real-Number System
2(6)
Real Numbers / Interval Notation / Properties of the Real Numbers / Absolute Value
R.2 Integer Exponents, Scientific Notation, and Order of Operations
8(9)
Integers as Exponents / Scientific Notation / Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
17(5)
Polynomials / Addition and Subtraction / Multiplication
R.4 Factoring
22(8)
Terms with Common Factors / Factoring by Grouping / Trinomials of the Type x2 + bx + c / Trinomials of the Type ax2 + bx + c, a ≠ 1 / Special Factorizations
R.5 The Basics of Equation Solving
30(5)
Linear Equations and Quadratic Equations / Formulas
R.6 Rational Expressions
35(9)
The Domain of a Rational Expression / Simplifying, Multiplying, and Dividing Rational Expressions / Adding and Subtracting Rational Expressions / Complex Rational Expressions
R.7 Radical Notation and Rational Exponents
44(13)
Simplifying Radical Expressions / An Application / Rationalizing Denominators or Numerators / Rational Exponents
Study Guide
53(1)
Review Exercises
54(2)
Chapter Test
56(1)
1 Graphs, Functions, and Models
57(102)
1.1 Introduction to Graphing
58(16)
Graphs / Solutions of Equations / Graphs of Equations / The Distance Formula / Midpoints of Segments / Circles
Visualizing the Graph
69(5)
1.2 Functions and Graphs
74(16)
Functions / Notation for Functions / Graphs of Functions / Finding Domains of Functions / Visualizing Domain and Range / Applications of Functions
1.3 Linear Functions, Slope, and Applications
90(17)
Linear Functions / The Linear Function f(x) = mx + b and Slope / Applications of Slope / Slope-Intercept Equations of Lines / Graphing f(x) = mx + b Using m and b / Applications of Linear Functions
Visualizing the Graph
101(5)
Mid-Chapter Mixed Review
106(1)
1.4 Equations of Lines and Modeling
107(14)
Slope-Intercept Equations of Lines / Point-Slope Equations of Lines / Parallel Lines / Perpendicular Lines / Mathematical Models / Curve Fitting / Linear Regression
1.5 Linear Equations, Functions, Zeros, and Applications
121(18)
Linear Equations / Applications Using Linear Models / Zeros of Linear Functions
1.6 Solving Linear Inequalities
139(20)
Linear Inequalities / Compound Inequalities / An Application
Study Guide
144(7)
Review Exercises
151(4)
Chapter Test
155(4)
2 More on Functions
159(76)
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
160(15)
Increasing, Decreasing, and Constant Functions / Relative Maximum and Minimum Values / Applications of Functions / Functions Defined Piecewise
2.2 The Algebra of Functions
175(7)
The Algebra of Functions: Sums, Differences, Products, and Quotients / Difference Quotients
2.3 The Composition of Functions
182(10)
The Composition of Functions / Decomposing a Function as a Composition
Mid-Chapter Mixed Review
190(2)
2.4 Symmetry
192(7)
Symmetry / Even Functions and Odd Functions
2.5 Transformations
199(14)
Transformations of Functions / Vertical Translations and Horizontal Translations / Reflections / Vertical and Horizontal Stretchings and Shrinkings
Visualizing the Graph
209(4)
2.6 Variation and Applications
213(22)
Direct Variation / Inverse Variation / Combined Variation
Study Guide
222(7)
Review Exercises
229(4)
Chapter Test
233(2)
3 Quadratic Functions and Equations; Inequalities
235(62)
3.1 The Complex Numbers
236(7)
The Complex-Number System / Addition and Subtraction / Multiplication / Conjugates and Division
3.2 Quadratic Equations, Functions, Zeros, and Models
243(16)
Quadratic Equations and Quadratic Functions / Completing the Square / Using the Quadratic Formula / The Discriminant / Equations Reducible to Quadratic / Applications
3.3 Analyzing Graphs of Quadratic Functions
259(16)
Graphing Quadratic Functions of the Type f(x) = a(x - h)2 + k / Graphing Quadratic Functions of the Type f{x) = ax2 + bx + c, a ≠ 0 / Applications
Visualizing the Graph
269(4)
Mid-Chapter Mixed Review
273(2)
3.4 Solving Rational Equations and Radical Equations
275(8)
Rational Equations / Radical Equations
3.5 Solving Equations and Inequalities with Absolute Value
283(14)
Equations with Absolute Value / Inequalities with Absolute Value
Study Guide
287(6)
Review Exercises
293(2)
Chapter Test
295(2)
4 Polynomial Functions and Rational Functions
297(94)
4.1 Polynomial Functions and Modeling
298(17)
The Leading-Term Test / Finding Zeros of Factored Polynomial Functions / Finding Real Zeros on a Calculator / Polynomial Models
4.2 Graphing Polynomial Functions
315(10)
Graphing Polynomial Functions / The Intermediate Value Theorem
Visualizing the Graph
322(3)
4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
325(10)
Division and Factors / The Remainder Theorem and Synthetic Division / Finding Factors of Polynomials
Mid-Chapter Mixed Review
333(2)
4.4 Theorems about Zeros of Polynomial Functions
335(10)
The Fundamental Theorem of Algebra / Finding Polynomials with Given Zeros / Zeros of Polynomial Functions with Real Coefficients / Rational Coefficients / Integer Coefficients and the Rational Zeros Theorem / Descartes' Rule of Signs
4.5 Rational Functions
345(20)
The Domain of a Rational Function / Asymptotes / Applications
Visualizing the Graph
361(4)
4.6 Polynomial Inequalities and Rational Inequalities
365(26)
Polynomial Inequalities / Rational Inequalities
Study Guide
375(10)
Review Exercises
385(4)
Chapter Test
389(2)
5 Exponential Functions and Logarithmic Functions
391(92)
5.1 Inverse Functions
392(12)
Inverses / Inverses and One-to-One Functions / Finding Formulas for Inverses / Inverse Functions and Composition / Restricting a Domain
5.2 Exponential Functions and Graphs
404(13)
Graphing Exponential Functions / Applications / The Number e / Graphs of Exponential Functions, Base e
5.3 Logarithmic Functions and Graphs
417(18)
Logarithmic Functions / Finding Certain Logarithms / Converting Between Exponential Equations and Logarithmic Equations / Finding Logarithms on a Calculator / Natural Logarithms / Changing Logarithmic Bases / Graphs of Logarithmic Functions / Applications
Visualizing the Graph
429(4)
Mid-Chapter Mixed Review
433(2)
5.4 Properties of Logarithmic Functions
435(8)
Logarithms of Products / Logarithms of Powers / Logarithms of Quotients / Applying the Properties / Simplifying Expressions of the Type loga ax and alogax
5.5 Solving Exponential Equations and Logarithmic Equations
443(10)
Solving Exponential Equations / Solving Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest
453(30)
Population Growth / Interest Compounded Continuously / Models of Limited Growth / Exponential Decay / Exponential and Logarithmic Curve Fitting
Study Guide
470(7)
Review Exercises
477(4)
Chapter Test
481(2)
6 The Trigonometric Functions
483(106)
6.1 Trigonometric Functions of Acute Angles
484(12)
The Trigonometric Ratios / The Six Functions Related / Function Values of 30°, 45°, and 60° / Function Values of Any Acute Angle / Cofunctions and Complements
6.2 Applications of Right Triangles
496(13)
Solving Right Triangles / Applications
6.3 Trigonometric Functions of Any Angle
509(18)
Angles, Rotations, and Degree Measure / Trigonometric Functions of Angles or Rotations / The Six Functions Related / Terminal Side on an Axis / Reference Angles: 30°, 45°, and 60° / Function Values for Any Angle
Mid-Chapter Mixed Review
525(2)
6.4 Radians, Arc Length, and Angular Speed
527(15)
Distances on the Unit Circle / Radian Measure / Arc Length and Central Angles / Linear Speed and Angular Speed
6.5 Circular Functions: Graphs and Properties
542(15)
Reflections on the Unit Circle / Finding Function Values / Graphs of the Sine and Cosine Functions / Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Graphs of Transformed Sine Functions and Cosine Functions
557(32)
Variations of Basic Graphs / Graphs of Sums: Addition of Ordinates / Damped Oscillation: Multiplication of Ordinates
Visualizing the Graph
570(4)
Study Guide
574(10)
Review Exercises
584(3)
Chapter Test
587(2)
7 Trigonometric Identities, Inverse Functions, and Equations
589(66)
7.1 Identities: Pythagorean and Sum and Difference
590(13)
Pythagorean Identities / Simplifying Trigonometric Expressions / Sum and Difference Identities
7.2 Identities: Cofunction, Double-Angle, and Half-Angle
603(9)
Cofunction Identities / Double-Angle Identities / Half-Angle Identities
7.3 Proving Trigonometric Identities
612(9)
The Logic of Proving Identities / Proving Identities / Product-to-Sum and Sum-to-Product Identities
Mid-Chapter Mixed Review
619(2)
7.4 Inverses of the Trigonometric Functions
621(11)
Restricting Ranges to Define Inverse Functions / Composition of Trigonometric Functions and Their Inverses
7.5 Solving Trigonometric Equations
632(23)
Visualizing the Graph
640(4)
Study Guide
644(7)
Review Exercises
651(3)
Chapter Test
654(1)
8 Applications of Trigonometry
655(86)
8.1 The Law of Sines
656(13)
Solving Oblique Triangles / The Law of Sines / Solving Triangles (AAS and ASA) / Solving Triangles (SSA) / The Area of a Triangle
8.2 The Law of Cosines
669(10)
The Law of Cosines / Solving Triangles (SAS) / Solving Triangles (SSS)
8.3 Complex Numbers: Trigonometric Notation
679(12)
Graphical Representation / Trigonometric Notation for Complex Numbers / Multiplication and Division with Trigonometric Notation / Powers of Complex Numbers / Roots of Complex Numbers
Mid-Chapter Mixed Review
689(2)
8.4 Polar Coordinates and Graphs
691(11)
Polar Coordinates / Polar Equations and Rectangular Equations / Graphing Polar Equations
Visualizing the Graph
699(3)
8.5 Vectors and Applications
702(8)
Vectors / Vector Addition / Applications / Components
8.6 Vector Operations
710(31)
Position Vectors / Operations on Vectors / Unit Vectors / Direction Angles / Angle Between Vectors / Forces in Equilibrium
Study Guide
725(11)
Review Exercises
736(4)
Chapter Test
740(1)
9 Systems of Equations and Matrices
741(94)
9.1 Systems of Equations in Two Variables
742(16)
Solving Systems of Equations Graphically / The Substitution Method / The Elimination Method / Applications
Visualizing the Graph
752(6)
9.2 Systems of Equations in Three Variables
758(10)
Solving Systems of Equations in Three Variables / Applications / Mathematical Models and Applications
9.3 Matrices and Systems of Equations
768(8)
Matrices and Row-Equivalent Operations / Gaussian Elimination with Matrices / Gauss-Jordan Elimination
9.4 Matrix Operations
776(13)
Matrix Addition and Subtraction / Scalar Multiplication / Products of Matrices / Matrix Equations
Mid-Chapter Mixed Review
787(2)
9.5 Inverses of Matrices
789(7)
The Identity Matrix / The Inverse of a Matrix / Solving Systems of Equations
9.6 Determinants and Cramer's Rule
796(8)
Determinants of Square Matrices / Evaluating Determinants Using Cofactors / Cramer's Rule
9.7 Systems of Inequalities and Linear Programming
804(12)
Graphs of Linear Inequalities / Systems of Linear Inequalities / Applications: Linear Programming
9.8 Partial Fractions
816(19)
Partial Fraction Decompositions
Study Guide
822(6)
Review Exercises
828(4)
Chapter Test
832(3)
10 Analytic Geometry Topics
835(76)
10.1 The Parabola
836(8)
Parabolas / Finding Standard Form by Completing the Square / Applications
10.2 The Circle and the Ellipse
844(9)
Circles / Ellipses / Applications
10.3 The Hyperbola
853(10)
Standard Equations of Hyperbolas / Applications
10.4 Nonlinear Systems of Equations and Inequalities
863(13)
Nonlinear Systems of Equations / Modeling and Problem Solving / Nonlinear Systems of Inequalities
Visualizing the Graph
870(5)
Mid-Chapter Mixed Review
875(1)
10.5 Rotation of Axes
876(8)
Rotation of Axes / The Discriminant
10.6 Polar Equations of Conics
884(6)
Polar Equations of Conics / Converting from Polar Equations to Rectangular Equations / Finding Polar Equations of Conics
10.7 Parametric Equations
890(21)
Graphing Parametric Equations / Determining a Rectangular Equation for Given Parametric Equations / Determining Parametric Equations for a Given Rectangular Equation / Applications
Study Guide
898(6)
Review Exercises
904(4)
Chapter Test
908(3)
11 Sequences, Series, and Combinatorics
911(80)
11.1 Sequences and Series
912(8)
Sequences / Finding the General Term / Sums and Series / Sigma Notation / Recursive Definitions
11.2 Arithmetic Sequences and Series
920(9)
Arithmetic Sequences / Sum of the First n Terms of an Arithmetic Sequence / Applications
11.3 Geometric Sequences and Series
929(12)
Geometric Sequences / Sum of the First n Terms of a Geometric Sequence / Infinite Geometric Series / Applications
Visualizing the Graph
937(4)
11.4 Mathematical Induction
941(6)
Proving Infinite Sequences of Statements
Mid-Chapter Mixed Review
946(1)
11.5 Combinatorics: Permutations
947(10)
Permutations / Factorial Notation / Permutations of n Objects Taken k at a Time / Permutations of Sets with Nondistinguishable Objects
11.6 Combinatorics: Combinations
957(6)
Combinations
11.7 The Binomial Theorem
963(8)
Binomial Expansions Using Pascal's Triangle / Binomial Expansion Using Combination Notation / Finding a Specific Term / Total Number of Subsets
11.8 Probability
971(20)
Experimental Probability and Theoretical Probability / Computing Experimental Probabilities / Theoretical Probability
Study Guide
981(4)
Review Exercises
985(3)
Chapter Test
988(3)
Photo Credits 991
Answers 1(1)
Index 1(12)
Index of Applications 13
Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University-Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife, Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters. Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University-Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children's camp. David Ellenbogen has taught math at the college level for twenty-two years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has also taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979. He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from The University of Massachusetts at Amherst. A co-founder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont. In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing. He has two sons, Monroe and Zack. Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University-Purdue University Indianapolis and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit, and spend time with her children.