Precalculus: Graphs and Models

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  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 2008-02-29
  • Publisher: McGraw-Hill Education

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TheBarnett Graphs & Modelsseries in college algebra and precalculus maximizes student comprehension by emphasizing computational skills, real-world data analysis and modeling, and problem solving rather than mathematical theory. Many examples feature side-by-side algebraic and graphical solutions, and each is followed by a matched problem for the student to work. This active involvement in the learning process helps students develop a more thorough understanding of concepts and processes.A hallmark of the Barnett series, the function concept serves as a unifying theme. A major objective of this book is to develop a library of elementary functions, including their important properties and uses. Employing this library as a basic working tool, students will be able to proceed through this course with greater confidence and understanding as they first learn to recognize the graph of a function and then learn to analyze the graph and use it to solve the problem. Applications included throughout the text give the student substantial experience in solving and modeling real world problems in an effort to convince even the most skeptical student that mathematics is really useful.

Table of Contents

Graphs and Models
Functions, graphs, and models
Using Graphing Utilities
Graphs and Properties
Graphs and Transformations
Operations on Functions; Composition
Inverse Functions
Group Activity
Mathematical Modeling–Choosing a Long Distance Calling Plan
Modeling with linear and quadratic functions
Linear Functions
Linear Equations and Models
Quadratic Functions
Complex Numbers
Quadratic Equations and Models
Additional Equation Solving Techniques
Solving Inequalities
Group Activity
Mathematical Modeling in Population Studies Cumulative Review Exercise for Chapters
and 2
Polynomial and rational functions
Polynomial Functions And Models
Polynomial Division
Real Zeros and Polynomial Inequalities
Complex Zeros and Rational Zeros of Polynomials
Rational Functions and Inequalities
Variation and Modeling
Group Activity
Interpolating Polynomials
Modeling with exponential and logarithmic functions
Exponential Functions
Exponential Models
Logarithmic Functions
Logarithmic Models
Exponential and Logarithmic Equations
Group Activity
Comparing Regression Models Cumulative Review Exercise for Chapters 3 and 4
Trigonometric functions
Angles and Their Measure
Trigonometric Functions
A Unit Circle Approach
Solving Right Triangles
Properties of Trigonometric Functions
More General Trigonometric Functions and and Models
Inverse Trigonometric Functions
Group Activity
A Predator-Prey Analysis Involving Mountain Lions and Deer
Trigonometric identities and conditional equations
Basic Identities and Their Use
Sum, Difference, and Cofunction Identities
Double-Angle and Half-Angle Identities
Product-Sum and Sum-Product Identities
Trigonometric Equations
Group Activity
From M sin Bt + N cos Bt to A sin (Bt + C)
A Harmonic Analysis Tool
Additional topics in trigonometry
Law of Sines
Law of Cosines
Vectors in the Plane
Polar Coordinates and Graphs
Complex Numbers and De Moivre's Theorem
Group Activity
Conic Sections and Planetary Orbits Cumulative Review Exercise for Chapters 5, 6, and 7
Modeling with systems of equations and inequalities
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Three Variables
Systems of Linear Inequalities
Linear Programming
Group Activity
Modeling with Systems of Equations
Matrices and determinants
Matrix Solutions to Linear Systems
Matrix Operations
Inverse of a Square Matrix
Matrix Equations and Systems of Linear Equations
Properties of Determinants
Determinants and Cramer's Rule
Group Activity
Using Matrices to Find Cost, Revenue, and Profit Cumulative Review Exercise for Chapters8 and 9
SEquences, induction, probability
Sequences and Series
Mathematical Induction
Arithmetic and Geometric Sequences
Multiplication Principle, Permutations, and Combinations
Sample Spaces and Probability
Binomial Formula
Group Activity
Sequences Specified by Recursion Formulas
Conic Sections; Parabola
Translation and Rotation of Axes
Systems of Nonlinear Equations
Review Chapte
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