Loose Leaf Version for Precalculus: Graphs & Models

Precalculus: Graphs & Models

Chapter 1: Functions and Graphs

Rectangular Coordinates, Graphing Circles and Other Relations

Functions, Function Notation, and the Graph of a Function

Linear Equations and Rates of Change

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

Solving Equations and Inequalities Graphically; Formulas and Problem Solving

Linear Models and Real Data

Chapter 2: Relations, More on Functions

Analyzing the Graph of a Function

The Toolbox Functions and Transformations

Absolute Value Functions, Equations, and Inequalities

Rational and Radical Functions; More on the Domain

Piecewise-Defined Functions

Variation: The Toolbox Functions in Action

Chapter 3: Quadratic Functions and Operations on Functions

complex Numbers

Solving Quadratic Equations and Inequalities

Quadratic Functions and Applications

Quadratic Models; More on Rates of Change

The Algebra of Functions

Composition of Functions and the Difference Quotient

Chapter 4: Polynomial and Rational Functions

Synthetic Division; the Remainder and Factor Theorems

The Zeros of Polynomial Functions

Graphing Polynomial Functions

Graphing Rational Functions

Additional Insights into Rational Functions

Polynomial and Rational Inequalities

Chapter 5: Exponential and Logarithmic Functions

One-to-One and Inverse Functions

Exponential Functions

Logarithms and Logarithmic Functions

Properties of Logarithms

Solving Exponential/Logarithmic Equations

Applications from Business, Finance, and Science

Exponential, Logarithmic, and Logistic Equation Models

Chapter 6: Introduction to Trigonometry

Angle Measure, Special Triangles, and Special Angles

Unit Circles and the Trigonometry of Real Numbers

Graphs of Sine and Cosine Functions

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

Translations and Applications of Trigonometric Graphs

The Trigonometry of Right Triangles

Trigonometry and the Coordinate Plane

Chapter 7: Trigonometric Identities, Inverses, and Equations

Fundamental Identities and Families of Identities

Constructing and Verifying Identities

The Sum and Difference Identities

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

Inverse Trigonometric Functions and their Applications

Solving Basic Trig Equations

General Trig Equations and Applications

Chapter 8: Applications of Trigonometry

Oblique Triangles and the Law of Sines

The Law of Cosines; the Area of a Triangle

Vectors and Vector Diagrams

Vectors Applications and the Dot Product

Complex Numbers in Trigonometric Form

DeMoivre’s Theorem and the Theorem on Nth Roots

Chapter 9: Systems of Equations ad Inequalities; Matrices

Systems of Equations in Two Variables

Systems of Equations in Three Variables

Partial Fraction Decomposition

Linear Inequalities and Linear Programming

Matrices and Row Operations

The Algebra of Matrices

Linear Systems and Matrix Equations

Applications of Matrices and Determinants

Chapter 10: Analytical Geometry; Polar and Parametric Equations

An Introduction to Analytic Geometry

The Circle and the Ellipse

The Hyperbola

The Analytic Parabola

Non-Linear Systems of Equations and Inequalities

Polar Coordinates, Equations, and Graphs

Rotation of Axes and Polar Form

Parametric Equations and Graphs

Chapter 11: Sequences, Series, Counting, and Probability

Sequences and Series

Arithmetic Sequences

Geometric Sequences

Mathematical Induction

Counting Techniques

Introduction to Probability

The Binomial Theorem

Chapter 12: Bridges to Calculus – An Introduction to Limits

Finding Limits Numerically and Graphically

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

Infinite Limits and Limits at Infinity

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

Appendix A: A Review of Basic Concepts and Skills

The Language, Notation, and Numbers of Mathematics

Algebraic Expressions, and the Properties of Real Numbers

Exponents, Scientific Notation, and a Review of Polynomials

Solving Linear Equations

Factoring Polynomials and Solving Equations by Factoring

Rational Expressions and Equations

Radicals, Rational Exponents, and Radical Equations

Geometry Review with Unit Conversions

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

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.