Precalculus: Graphs & Models

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2011-03-04
  • Publisher: McGraw-Hill Education
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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.

Table of Contents

Precalculus: Graphs & Models

Chapter 1: Functions and Graphs

1.1, Rectangular Coordinates; Graphing Circles and Other Relations

1.2, Linear Equations and Rates of Change

1.3, Functions, Function Notation, and the Graph of a Function

1.4, Linear Functions, Special Forms, and More on Rates of Change

1.5, Solving Equations and Inequalities Graphically; Formulas and Problem Solving

1.6, Linear Function Models and Real Data

Chapter 2: Relations, More on Functions

2.1, Analyzing the Graph of a Function

2.2, The Toolbox Functions and Transformations

2.3, Absolute Value Functions, Equations, and Inequalities

2.4, Rational and Radical Functions; More on the Domain

2.5, Piecewise-Defined Functions

2.6, Variation: The Toolbox Functions in Action

Chapter 3: Quadratic Functions and Operations on Functions

3.1, Complex Numbers

3.2, Solving Quadratic Equations and Inequalities

3.3, Quadratic Functions and Applications

3.4, Quadratic Models; More on Rates of Change

3.5, The Algebra of Functions

3.6, Composition of Functions and the Difference Quotient

Chapter 4: Polynomial and Rational Functions

4.1, Synthetic Division; the Remainder and Factor Theorems

4.2, The Zeros of Polynomial Functions

4.3, Graphing Polynomial Functions

4.4, Graphing Rational Functions

4.5, Additional Insights into Rational Functions

4.6, Polynomial and Rational Inequalities

Chapter 5: Exponential and Logarithmic Functions

5.1, One-to-One and Inverse Functions

5.2, Exponential Functions

5.3, Logarithms and Logarithmic Functions

5.4, Properties of Logarithms

5.5, Solving Exponential and Logarithmic Equations

5.6, Applications from Business, Finance, and Science

5.7, Exponential, Logarithmic, and Logistic Equation Models

Chapter 6: Introduction to Trigonometry

6.1, Angle Measure, Special Triangles, and Special Angles

6.2, Unit Circles and the Trigonometry of Real Numbers

6.3, Graphs of Sine and Cosine Functions

6.4, Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions

6.5, Transformations and Applications of Trigonometric Graphs

6.6, The Trigonometry of Right Triangles

6.7, Trigonometry and the Coordinate Plane

6.8, Trigonometric Equation Models

Chapter 7: Trigonometric Identities, Inverses, and Equations

7.1, Fundamental Identities and Families of Identities

7.2, More on Verifying Identities

7.3, The Sum and Difference Identities

7.4, The Double-Angle, Half-Angle and Product-to-Sum Identities

7.5, The Inverse Trigonometric Functions and their Applications

7.6, Solving Basic Trig Equations

7.7, General Trig Equations and Applications

Chapter 8: Applications of Trigonometry

8.1, Oblique Triangles and the Law of Sines

8.2, The Law of Cosines; the Area of a Triangle

8.3, Vectors and Vector Diagrams

8.4, Vector Applications and the Dot Product

8.5, Complex Numbers in Trigonometric Form

8.6, De Moivre’s Theorem and the Theorem on nth Roots

Chapter 9: Systems of Equations ad Inequalities; Matrices

9.1, Linear Systems in Two Variables with Applications

9.2, Linear Systems in Three Variables with Applications

9.3, Systems of Inequalities and Linear Programming

9.4, Partial Fraction Decomposition

9.5, Solving Linear Systems Using Matrices and Row Operations

9.6, The Algebra of Matrices

9.7, Solving Linear Systems Using Matrix Equations

9.8, Applications of Matrices and Determinants: Cramer’s Rule, Geometry, and More

Chapter 10: Analytical Geometry; Polar and Parametric Equations

10.1, A Brief Introduction to Analytic Geometry

10.2, The Circle and the Ellipse

10.3, The Hyperbola

10.4, The Analytic Parabola

10.5, Nonlinear Systems of Equations and Inequalities

10.6, Polar Coordinates, Equations, and Graphs

10.7, More on the Conic Sections: Rotation of Axes and Polar Form

10.8, Parametric Equations and Graphs

Chapter 11: Sequences, Series, Counting, and Probability

11.1, Sequences and Series

11.2, Arithmetic Sequences

11.3, Geometric Sequences

11.4, Mathematical Induction

11.5, Counting Techniques

11.6, Introduction to Probability

11.7, The Binomial Theorem

Chapter 12: Bridges to Calculus – An Introduction to Limits

12.1, Finding Limits Numerically and Graphically

12.2, Algebraic Methods for Finding Limits; One-Sided Limits and Continuity

12.3, Infinite Limits and Limits at Infinity

12.4, Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve

Appendix A: A Review of Basic Concepts and Skills

A.1, Algebraic Expressions and the Properties of Real Numbers

A.2, Exponents, Scientific Notation, and a Review of Polynomials

A.3, Solving Linear Equations and Inequalities

A.4, Factoring Polynomials and Solving Equations by Factoring

A.5, Rational Expressions and Equations

A.6, Radicals, Rational Exponents, and Radical Equations

Appendix B: Proof Positive!

Appendix C: More on Synthetic Division

Appendix D: Reduced Row-Echelon Form and More on Matrices

Appendix E: The Equation of a Conic

Appendix F: Sinusoidal Regression Models

Online Appendices

AO.1, The Language, Notation, and Numbers of Mathematics

AO.2, Geometry Review with Unit Conversions

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