# Graphical Approach to College Algebra & Trigonometry, A

• ISBN13:

• ISBN10:

## 0201735105

• Edition: 3rd
• Format: Hardcover
• Purchase Benefits
• Free Shipping On Orders Over \$35!
Your order must be \$35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
• Get Rewarded for Ordering Your Textbooks! Enroll Now
List Price: \$144.00

### Summary

This series is the culmination of many years of teaching experience with the graphing calculator. the books were written from the beginning for use with the graphing calculator. Throughout the text, the authors emphasize the power of technology but provide numerous warnings of its limitations: they stress that only through understanding the mathematical concepts can students fully appreciate the power of graphing calculators and use technology appropriately. Additionally, the authors consistently use the same four-step process when introducing the different classes of functions. This allows students to easily make connections between graphs of functions and their associated equations and inequalities.

 Linear Functions, Equations, and Inequalities
1(89)
 Real Numbers and Coordinate Systems
2(9)
 Sets of Real Numbers
 Coordinate Systems
 Viewing Windows
 Roots
 Distance and Midpoint Formulas
 Introduction to Relations and Functions
11(12)
 Set-Builder Notation and Interval Notation
 Relations, Domain, and Range
 Functions
 Tables
 Function Notation
 Reviewing Basic Concepts (Sections 1.1 and 1.2)
23(1)
 Linear Functions
23(13)
 Slope of a Line
 Slope-Intercept Form of the Equation of a Line
 Equations of Lines and Linear Models
36(15)
 Point-Slope Form of the Equation of a Line
 Other Forms of the Equation of a Line
 Parallel and Perpendicular Lines
 Linear Models and Regression
 Reviewing Basic Concepts (Sections 1.3 and 1.4)
51(1)
 Linear Equations and Inequalities
51(16)
 Solving Linear Equations
 Graphical Approaches to Solving Linear Equations
 Solving Linear Inequalities
 Graphical Approaches to Solving Linear Inequalities
 Three-Part Inequalities
 Applications of Linear Functions
67(22)
 Problem-Solving Strategies
 Applications of Linear Equations
 Break-Even Analysis
 Direct Variation
 Formulas
 Reviewing Basic Concepts (Sections 1.5 and 1.6)
77(1)
 Chapter 1 Summary
78(4)
 Chapter 1 Review Exercises
82(4)
 Chapter 1 Test
86(2)
 Chapter 1 Project Predicting Heights and Weights of Athletes
88(1)
 Analysis of Graphs of Functions
89(83)
 Graphs of Basic Functions and Relations; Symmetry
90(14)
 Continuity
 Increasing and Decreasing Functions
 The Identity Function
 The Squaring Function and Symmetry with Respect to the y-Axis
 The Cubing Function and Symmetry with Respect to the Origin
 The Square Root and Cube Root Functions
 The Absolute Value Function
 The Relation x = y2 and Symmetry with Respect to the x-Axis
 Even and Odd Functions
 Vertical and Horizontal Shifts of Graphs
104(10)
 Vertical Shifts
 Horizontal Shifts
 Combinations of Vertical and Horizontal Shifts
 Effects of Shifts on Domain and Range
 Horizontal Shifts Applied to Equations for Modeling
 Stretching, Shrinking, and Reflecting Graphs
114(12)
 Vertical Stretching
 Vertical Shrinking
 Reflecting Across an Axis
 Combining Transformations of Graphs
 Reviewing Basic Concepts (Sections 2.1 -- 2.3)
124(2)
 Absolute Value Functions: Graphs, Equations, Inequalities, and Applications
126(11)
 The Graph of y = |f(x)|
 Properties of Absolute Value
 Equations and Inequalities Involving Absolute Value
 An Application Involving Absolute Value
 Piecewise-Defined Functions
137(11)
 Graphing Piecewise-Defined Functions
 The Greatest Integer Function
 Applications of Piecewise-Defined Functions
 Operations and Composition
148(24)
 Operations on Functions
 The Difference Quotient
 Composition of Functions
 Applications of Operations and Composition
 Reviewing Basic Concepts (Sections 2.4--2.6)
161(1)
 Chapter 2 Summary
162(3)
 Chapter 2 Review Exercises
165(3)
 Chapter 2 Test
168(1)
 Chapter 2 Project Modeling the Movement of a Cold Front
169(3)
 Polynomial Functions
172(100)
 Complex Numbers
173(7)
 The Number i
 Operations with Complex Numbers
180(13)
 Completing the Square
 Vertex Formula
 Extreme Values
 Applications and Modeling
193(14)
 Zero-Product Property
 Solving x2 = k
 Reviewing Basic Concepts (Sections 3.1--3.3)
207(1)
 Further Applications of Quadratic Functions and Models
207(10)
 Higher-Degree Polynomial Functions and Graphs
217(15)
 Cubic Functions
 Quartic Functions
 Extrema
 End Behavior
 x-Intercepts (Real Zeros)
 Comprehensive Graphs
 Curve Fitting and Polynomial Models
 Reviewing Basic Concepts (Sections 3.4 and 3.5)
231(1)
 Topics in the Theory of Polynomial Functions (I)
232(10)
 Intermediate Value Theorem
 Division of Polynomials and Synthetic Division
 Remainder and Factor Theorems
 Topics in the Theory of Polynomial Functions (II)
242(9)
 Complex Zeros and the Fundamental Theorem of Algebra
 Number of Zeros
 Rational Zeros Theorem
 Polynomial Equations and Inequalities; Further Applications and Models
251(21)
 Polynomial Equations and Inequalities
 Complex nth Roots
 Applications and Polynomial Models
 Reviewing Basic Concepts (Sections 3.6--3.8)
261(1)
 Chapter 3 Summary
262(3)
 Chapter 3 Review Exercises
265(4)
 Chapter 3 Test
269(1)
 Chapter 3 Project Creating a Social Security Polynomial
270(2)
 Rational, Power, and Root Functions
272(70)
 Rational Functions and Graphs
273(6)
 The Reciprocal Function
 The Rational Function Defined by f(x) = 1/x2
 Mode and Window Choices for Calculator Graphs
 More on Graphs of Rational Functions
279(14)
 Vertical and Horizontal Asymptotes
 Graphing Techniques
 Oblique Asymptotes
 Graphs with Points of Discontinuity
 Rational Equations, Inequalities, Applications, and Models
293(16)
 Solving Rational Equations and Inequalities
 Applications and Models of Rational Functions
 Inverse Variation
 Combined and Joint Variation
 Reviewing Basic Concepts (Sections 4.1--4.3)
308(1)
 Functions Defined by Powers and Roots
309(11)
 Power and Root Functions
 Modeling Using Power Functions
 Graphs of
 Graphing Circles and Horizontal Parabolas Using Root Functions
 Equations, Inequalities, and Applications Involving Root Functions
320(22)
 Equations and Inequalities
 Applications
 Reviewing Basic Concepts (Sections 4.4 and 4.5)
330(1)
 Chapter 4 Summary
331(2)
 Chapter 4 Review Exercises
333(4)
 Chapter 4 Test
337(2)
 Chapter 4 Project How Rugged Is Your Coastline?
339(3)
 Inverse, Exponential, and Logarithmic Functions
342(77)
 Inverse Functions
343(10)
 Inverse Operations
 One-to-One Functions
 Inverse Functions and Their Graphs
 An Application of Inverse Functions
 Exponential Functions
353(12)
 Real-Number Exponents
 Graphs of Exponential Functions
 Exponential Equations (Type I)
 The Number e
 Compound Interest
 Logarithms and Their Properties
365(12)
 Definition of Logarithm
 Common Logarithms
 Natural Logarithms
 Properties of Logarithms
 Change-of-Base Rule
 Reviewing Basic Concepts (Sections 5.1--5.3)
376(1)
 Logarithmic Functions
377(9)
 Graphs of Logarithmic Functions
 Applying Earlier Work to Logarithmic Functions
 A Logarithmic Model
 Exponential and Logarithmic Equations and Inequalities
386(10)
 Exponential Equations and Inequalities (Type 2)
 Logarithmic Equations and Inequalities
 Equations and Inequalities Involving Both Exponentials and Logarithms
 Formulas Involving Exponentials and Logarithms
 Reviewing Basic Concepts (Sections 5.4 and 5.5)
395(1)
 Further Applications and Modeling with Exponential and Logarithmic Functions
396(23)
 Physical Science Applications
 Financial Applications
 Biological and Medical Applications
 Modeling Data with Exponential and Logarithmic Functions
 Chapter 5 Summary
410(3)
 Chapter 5 Review Exercises
413(3)
 Chapter 5 Test
416(1)
 Chapter 5 Project Modeling Motor Vehicle Sales in the United States (with a lesson about careless use of mathematical models)
417(2)
 Analytic Geometry
419(47)
 Circles and Parabolas
420(13)
 Conic Sections
 Equations and Graphs of Circles
 An Application of Circles
 Equations and Graphs of Parabolas
 An Application of Parabolas
 Ellipses and Hyperbolas
433(13)
 Equations and Graphs of Ellipses
 Applications of Ellipses
 Equations and Graphs of Hyperbolas
 Reviewing Basic Concepts (Sections 6.1 and 6.2)
446(1)
 Summary of the Conic Sections
446(8)
 Characteristics
 Identifying Conic Sections
 Eccentricity
 Parametric Equations
454(12)
 Graphs of Parametric Equations and Their Rectangular Equivalents
 Alternative Forms of Parametric Equations
 An Application
 Reviewing Basic Concepts (Sections 6.3 and 6.4)
459(1)
 Chapter 6 Summary
459(2)
 Chapter 6 Review Exercises
461(2)
 Chapter 6 Test
463(1)
 Chapter 6 Project Modeling the Path of a Bouncing Ball
464(2)
 Matrices and Systems of Equations and Inequalities
466(100)
 Systems of Equations
467(13)
 Linear Systems
 Substitution Method
 Elimination Method
 Special Systems
 Nonlinear Systems
 Applications of Systems
 Solution of Linear Systems by the Echelon Method
480(8)
 Geometric Considerations
 Analytic Solution of Systems in Three Variables
 Applications of Systems
 Curve Fitting Using a System
 Solution of Linear Systems by Row Transformations
488(13)
 Matrices and Technology
 Matrix Row Transformations
 Row Echelon Method
 Reduced Row Echelon Method
 Special Cases
 An Application
 Reviewing Basic Concepts (Sections 7.1--7.3)
501(1)
 Matrix Properties and Operations
501(15)
 Terminology of Matrices
 Operations on Matrices
 Applying Matrix Algebra
 Determinants and Cramer's Rule
516(11)
 Determinants of 2 X 2 Matrices
 Determinants of Larger Matrices
 Derivation of Cramer's Rule
 Using Cramer's Rule to Solve Systems
 Solution of Linear Systems by Matrix Inverses
527(11)
 Identity Matrices
 Multiplicative Inverses of Square Matrices
 Solving Linear Systems Using Inverse Matrices
 Curve Fitting Using a System
 Reviewing Basic Concepts (Sections 7.4--7.6)
537(1)
 Systems of Inequalities and Linear Programming
538(10)
 Solving Linear Inequalities
 Solving Systems of Inequalities
 Linear Programming
 Partial Fractions
548(18)
 Decomposition of Rational Expressions
 Distinct Linear Factors
 Repeated Linear Factors
 Reviewing Basic Concepts (Sections 7.7 and 7.8)
555(1)
 Chapter 7 Summary
556(2)
 Chapter 7 Review Exercises
558(4)
 Chapter 7 Test
562(1)
 Chapter 7 Project Finding a Polynomial Whose Graph Passes Through Any Number of Given Points
563(3)
 Trigonometric Functions and Applications
566(107)
 Angles and Their Measures
567(16)
 Basic Terminology
 Degree Measure
 Standard Position and Coterminal Angles
 Arc Lengths and Sectors
 Angular and Linear Speed
 Trigonometric Functions and Fundamental Identities
583(12)
 Trigonometric Functions
 Reciprocal Identities
 Signs and Ranges of Function Values
 Pythagorean Identities
 Quotient Identities
 Reviewing Basic Concepts (Sections 8.1 and 8.2)
594(1)
 Evaluating Trigonometric Functions
595(12)
 Definitions of the Trigonometric Functions
 Trigonometric Function Values of Special Angles
 Cofunction Identities
 Reference Angles
 Special Angles as Reference Angles
 Finding Function Values with a Calculator
 Finding Angle Measures
 Applications of Right Triangles
607(13)
 Significant Digits
 Solving Triangles
 Angles of Elevation or Depression
 Bearing
 Further Applications
 Reviewing Basic Concepts (Sections 8.3 and 8.4)
619(1)
 The Circular Functions
620(8)
 Circular Functions
 Applications of Circular Functions
 Graphs of the Sine and Cosine Functions
628(18)
 Periodic Functions
 Graph of the Sine Function
 Graph of the Cosine Function
 Graphing Techniques, Amplitude, and Period
 Translations
 Determining a Trigonometric Model Using Curve Fitting
 Reviewing Basic Concepts (Sections 8.5 and 8.6)
645(1)
 Graphs of the Other Circular Functions
646(10)
 Graphs of the Cosecant and Secant Functions
 Graphs of the Tangent and Cotangent Functions
 Harmonic Motion
656(17)
 Simple Harmonic Motion
 Damped Oscillatory Motion
 Reviewing Basic Concepts (Sections 8.7 and 8.8)
659(1)
 Chapter 8 Summary
660(4)
 Chapter 8 Review Exercises
664(5)
 Chapter 8 Test
669(2)
 Chapter 8 Project Modeling Sunset Times
671(2)
 Trigonometric Identities and Equations
673(66)
 Trigonometric Identities
674(10)
 Fundamental Identities
 Using the Fundamental Identities
 Verifying Identities
 Sum and Difference Identities
684(10)
 Cosine Sum and Difference Identities
 Sine and Tangent Sum and Difference Identities
 Reviewing Basic Concepts (Sections 9.1 and 9.2)
693(1)
 Further Identities
694(12)
 Double-Number Identities
 Product-to-Sum and Sum-to-Product Identities
 Half-Number Identities
 The Inverse Circular Functions
706(12)
 Inverse Sine Function
 Inverse Cosine Function
 Inverse Tangent Function
 Remaining Inverse Trigonometric Functions
 Inverse Function Values
 Reviewing Basic Concepts (Sections 9.3 and 9.4)
717(1)
 Trigonometric Equations and Inequalities (I)
718(6)
 Equations Solvable by Linear Methods
 Equations Solvable by Factoring
 Equations Solvable by the Quadratic Formula
 Using Trigonometric Identities to Solve Equations
 Trigonometric Equations and Inequalities (II)
724(15)
 Equations and Inequalities Involving Multiple-Number Identities
 Equations and Inequalities Involving Half-Number Identities
 An Application
 Reviewing Basic Concepts (Sections 9.5 and 9.6)
730(1)
 Chapter 9 Summary
731(2)
 Chapter 9 Review Exercises
733(3)
 Chapter 9 Test
736(1)
 Chapter 9 Project Modeling a Damped Pendulum
737(2)
 Applications of Trigonometry; Vectors
739(77)
 The Law of Sines
740(13)
 Congruency and Oblique Triangles
 Derivation of the Law of Sines
 Applications
 Ambiguous Case
 The Law of Cosines and Area Formulas
753(10)
 Derivation of the Law of Cosines
 Applications
 Area Formulas
 Vectors and Their Applications
763(13)
 Basic Terminology
 Algebraic Interpretation of Vectors
 Operations with Vectors
 Dot Product and the Angle between Vectors
 Applications of Vectors
 Reviewing Basic Concepts (Sections 10.1--10.3)
775(1)
 Trigonometric (Polar) Form of Complex Numbers
776(8)
 The Complex Plane and Vector Representation
 Trigonometric (Polar) Form
 Products of Complex Numbers in Trigonometric Form
 Quotients of Complex Numbers in Trigonometric Form
 Powers and Roots of Complex Numbers
784(7)
 Powers of Complex Numbers (De Moivre's Theorem)
 Roots of Complex Numbers
 Reviewing Basic Concepts (Sections 10.4 and 10.5)
790(1)
 Polar Equations and Graphs
791(10)
 Polar Coordinate System
 Graphs of Polar Equations
 Classifying Polar Equations
 Converting Equations
 More Parametric Equations
801(15)
 Parametric Equations with Trigonometric Functions
 The Cycloid
 Applications of Parametric Equations
 Reviewing Basic Concepts (Sections 10.6 and 10.7)
808(1)
 Chapter 10 Summary
808(3)
 Chapter 10 Review Exercises
811(3)
 Chapter 10 Test
814(1)
 Chapter 10 Project When Is a Circle Really a Polygon?
814(2)
 Further Topics in Algebra
816(74)
 Sequences and Series
817(10)
 Sequences
 Series and Summation Notation
 Summation Properties
 Arithmetic Sequences and Series
827(8)
 Arithmetic Sequences
 Arithmetic Series
 Geometric Sequences and Series
835(12)
 Geometric Sequences
 Geometric Series
 Infinite Geometric Series
 Annuities
 Reviewing Basic Concepts (Sections 11.1--11.3)
846(1)
 The Binomial Theorem
847(7)
 A Binomial Expansion Pattern
 Pascal's Triangle
 n-Factorial
 Binomial Coefficients
 The Binomial Theorem
 rth Term of a Binomial Expansion
 Mathematical Induction
854(7)
 Proof by Mathematical Induction
 Proving Statements
 Generalized Principle of Mathematical Induction
 Proof of the Binomial Theorem
 Reviewing Basic Concepts (Sections 11.4 and 11.5)
861(1)
 Counting Theory
861(9)
 Fundamental Principle of Counting
 Permutations
 Combinations
 Distinguishing between Permutations and Combinations
 Probability
870(20)
 Basic Concepts
 Complements and Venn Diagrams
 Odds
 Union of Two Events
 Binomial Probability
 Reviewing Basic Concepts (Sections 11.6 and 11.7)
881(1)
 Chapter 11 Summary
881(4)
 Chapter 11 Review Exercises
885(2)
 Chapter 11 Test
887(1)
 Chapter 11 Project Using Experimental Probabilities to Simulate Family Makeup
888(2)
Reference: Basic Algebraic Concepts and Geometry Formulas 890(36)
 Review of Exponents and Polynomials
891(6)
 Rules for Exponents
 Terminology for Polynomials
 Multiplying Polynomials
 Review of Factoring
897(7)
 Factoring Out the Greatest Common Factor
 Factoring by Grouping
 Factoring Trinomials
 Factoring Special Products
 Factoring by Substitution
 Review of Rational Expressions
904(7)
 Domain of a Rational Expression
 Lowest Terms of a Rational Expression
 Multiplying and Dividing Rational Expressions
 Complex Fractions
 Review of Negative and Rational Exponents
911(6)
 Negative Exponents and the Quotient Rule
 Rational Exponents
917(7)
 Rationalizing Denominators
 Geometry Formulas
924(2)
Appendix A: Vectors in Space 926(6)
Appendix B: Polar Form of Conic Sections 932(4)
Appendix C: Rotation of Axes 936
Index of Applications 1(6)
Index 7