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Record Nr. |
UNINA9910154799503321 |
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Autore |
Sullivan Michael |
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Titolo |
Precalculus : concepts through functions, a unit circle approach to trigonometry / / Michael Sullivan, Michael Sullivan III |
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Pubbl/distr/stampa |
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Boston : , : Pearson, , [2015] |
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©2015 |
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ISBN |
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Edizione |
[Third, global edition.] |
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Descrizione fisica |
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1 online resource (1,191 pages) : color illustrations |
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Collana |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Cover -- Title -- Copyright -- Contents -- To the Student -- Preface to the Instructor -- Prepare for Class ''Read the Book'' -- Practice ''Work the Problems'' -- Review ''Study for Quizzes and Tests'' -- Resources for Success -- Applications Index -- F Foundations: A Prelude to Functions -- F.1 The Distance and Midpoint Formulas -- Use the Distance Formula -- Use the Midpoint Formula -- F. 2 Graphs of Equations in Two Variables -- Intercepts -- Symmetry -- Graph Equations by Plotting Points -- Find Intercepts from a Graph -- Find Intercepts from an Equation -- Test an Equation for Symmetry -- Know How to Graph Key Equations -- F. 3 Lines -- Calculate and Interpret the Slope of a Line -- Graph Lines Given a Pointand the Slope -- Find the Equation of a Vertical Line -- Use the Point-Slope Form of a Line -- Identify Horizontal Lines -- Find the Equation of a Line Given Two Points -- Write the Equation of a Line in Slope-Intercept Form -- Identify the Slope and y-Intercept of a Line from Its Equation -- Graph Lines Written in General Form Using Intercepts -- Find Equations of Parallel Lines -- Find Equations of Perpendicular Lines -- F. 4 Circles -- Write the Standard Form of the Equation of a Circle -- Graph a Circle -- Work with the General Form of the Equation of a Circle -- Chapter Project -- 1 Functions and Their Graphs -- 1.1 Functions -- Determine Whether a Relation Represents a Function -- Find the Value of a Function -- Find the Domain of a Function Defined by an Equation -- Formthe Sum, Difference, Product, and Quotient of Two Functions -- |
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1.2 The Graph of a Function -- Identify the Graph of a Function -- Obtain Information from or about the Graph of a Function -- 1.3 Properties of Functions -- Determine Even and Odd Functions from a Graph -- Identify Even and Odd Functions from the Equation. |
Use a Graph to Determine Where a Function is Increasing, Decreasing, or Constant -- Use a Graph to Locate Local Maxima and Local Minima -- Use a Graph to Locate the Absolute Maximum and the Absolute Minimum -- Use a Graphing Utility to Approximate Local Maxima and Local Minima and to Determine Where a Function is Increasing or Decreasing -- Find the Average Rate of Change of a Function -- 1.4 Library of Functions -- Piecewise-defined Functions -- Graph the Functions Listed in the Library of Functions -- Graph Piecewise-defined Functions -- 1.5 Graphing Techniques: Transformations -- Graph Functions Using Vertical and Horizontal Shifts -- Graph Functions Using Compressions and Stretches -- Graph Functions Using Reflections about the x-Axis and the y-Axis -- 1.6 Mathematical Models: Building Functions -- Build and Analyze Functions -- 1.7 Building Mathematical Models Using Variation -- Construct a Model Using Direct Variation -- Construct a Model UsingInverse Variation -- Construct a Model Using Joint or Combined Variation -- Chapter Review -- Chapter Test -- Chapter Projects -- 2 Linear and Quadratic Functions -- 2.1 Properties of Linear Functions and Linear Models -- Graph Linear Functions -- Use Average Rate of Change to Identify Linear Functions -- Determine Whether a Linear Function Is Increasing, Decreasing or Constant -- Find the Zero of a Linear Function -- Build Linear Models from Verbal Descriptions -- 2.2 Building Linear Models from Data -- Draw and Interpret Scatter Diagrams -- Distinguish between Linear and Nonlinear Relations -- Use a Graphing Utility to Find the Line of Best Fit -- 2.3 Quadratic Functions and Their Zeros -- Find the Zeros of a Quadratic Function by Factoring -- Find the Zeros of a Quadratic Function Using the Square Root Method -- Find the Zeros of a Quadratic Function by Completing the Square. |
Find the Zeros of a Quadratic Function Using the Quadratic Formula -- Find the Point of Intersection of Two Functions -- Solve Equations That Are Quadratic in Form -- 2.4 Properties of Quadratic Functions -- Graph a Quadratic Function Using Transformations -- Identify the Vertexand Axis of Symmetry of a Quadratic Function -- Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts -- Find a Quadratic Function Given Its Vertex and One Other Point -- Find the Maximum or Minimum Value of a Quadratic Function -- 2.5 Inequalities Involving Quadratic Functions -- Solve Inequalities Involving a Quadratic Function -- 2.6 Building Quadratic Models from Verbal Descriptions and from Data -- Build Quadratic Models from Verbal Descriptions -- Build Quadratic Models from Data -- 2.7 Complex Zeros of a Quadratic Function -- Find the Complex Zeros of a Quadratic Function -- 2.8 Equations and Inequalities Involving the Absolute Value Function -- Solve Absolute Value Equations -- Solve Absolute Value Inequalities -- Chapter Review -- Chapter Test -- Cumulative Review -- Chapter Projects -- 3 Polynomial and Rational Functions -- 3.1 Polynomial Functions and Models -- Identify Polynomial Functions and Their Degree -- Graph Polynomial Functions Using Transformations -- Identify the Real Zeros of a Polynomial Function and Their Multiplicity -- Analyze the Graph of a Polynomial Function -- Build Cubic Models from Data -- 3.2 The Real Zeros of a Polynomial Function -- Use the Remainder and Factor Theorems -- Use Descartes' Rule of Signs to Determine the Number of Positive and the Number of Negative Real Zeros of a Polynomial Function -- Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function -- Find the |
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Real Zeros ofa Polynomial Function -- Solve Polynomial Equations -- Use the Theorem for Bounds on Zeros. |
Use the Intermediate Value Theorem -- 3.3 Complex Zeros -- Fundamental Theorem of Algebra -- Use the Conjugate Pairs Theorem -- Find a Polynomial Function with Specified Zeros -- Find the Complex Zeros of a Polynomial Function -- 3.4 Properties of Rational Functions -- Find the Domain of a Rational Function -- Find the Vertical Asymptotes of a Rational Function -- Find the Horizontal or Oblique Asymptote of a Rational Function -- 3.5 The Graph of a Rational Function -- Analyze the Graph of a Rational Function -- Solve Applied Problems Involving Rational Functions -- 3.6 Polynomial and Rational Inequalities -- Solve Polynomial Inequalities -- Solve Rational Inequalities -- Chapter Review -- Chapter Test -- Cumulative Review -- Chapter Projects -- 4 Exponential and Logarithmic Functions -- 4.1 Composite Functions -- Form a Composite Function -- Find the Domain of a Composite Function -- 4.2 One-to-One Functions -- Inverse Functions -- Determine Whether a Function Is One-to-One -- Determine the Inverse of a Function Defined by a Map or a Set of Ordered Pairs -- Obtain the Graph ofthe Inverse Function from the Graph of the Function -- Find the Inverse of a Function Defined by an Equation -- 4.3 Exponential Functions -- Evaluate Exponential Functions -- Graph Exponential Functions -- Define the Number e -- Solve Exponential Equations -- 4.4 Logarithmic Functions -- Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential Statements -- Evaluate Logarithmic Expressions -- Determine the Domain of a Logarithmic Function -- Graph Logarithmic Functions -- Solve Logarithmic Equations -- 4.5 Properties of Logarithms -- Work with Properties of Logarithms -- Write a Logarithmic Expression as a Sum or Difference of Logarithms -- Write a Logarithmic Expression as a Single Logarithm. |
Evaluate a Logarithm Whose Base Is Neither 10 Nor e -- Graph a Logarithmic Function Whose Base Is Neither 10 Nor e -- 4.6 Logarithmic and Exponential Equations -- Solve Logarithmic Equations -- Solve Exponential Equations -- Solve Logarithmic and Exponential Equations Using a Graphing Utility -- 4.7 Financial Models -- Determine the Future Value of a Lump Sum of Money -- Calculate Effective Rates of Return -- Determine the Present Value of a Lump Sum of Money -- Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money -- 4.8 Exponential Growth and Decay Models -- Newton's Law -- Logistic Growth and Decay Models -- Find Equations of Populations That Obey the Law of Uninhibited Growth -- Find Equations of Populations That Obey the Law of Decay -- Use Newton's Law of Cooling -- Use Logistic Models -- 4.9 Building Exponential, Logarithmic, and Logistic Models from Data -- Build an Exponential Model from Data -- Build a Logarithmic Model from Data -- Build a Logistic Model from Data -- Chapter Review -- Chapter Test -- Cumulative Review -- Chapter Projects -- 5 Trigonometric Functions -- 5.1 Angles and Their Measures -- Convert between Decimals and Degrees, Minutes, Seconds Measures for Angles -- Find the Length if an Arc of a Circle -- Convert from Degreesto Radians and from Radians to Degrees -- Find the Area of a Sector of a Circle -- Find the Linear Speed of an Object Traveling in Circular Motion -- 5.2 Trigonometric Functions: Unit Circle Approach -- Find the Exact Values of the Trigonometric Functions Using a Point on the Unit Circle -- Find the Exact Values of the Trigonometric Functions of Quadrantal Angles -- Find the Exact Values of the Trigonometric Functions -- Find the Exact Values of the Trigonometric Functions -- Find the Exact Values of the Trigonometric Functions for Integer Multiples. |
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Use a Calculator to Approximate the Value of a Trigonometric Function. |
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Sommario/riassunto |
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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry, Third Edition focuses on the fundamentals: preparation for class, practice with homework, and reviewing of key concepts. With the Concepts Through Functions series, the Sullivans expose students to functions in the first chapter and maintain a continuous theme of functions throughout the text. This approach ensures students master basic skills and develop the conceptual understanding they need for the course, ultimately preparing students for future math courses as well. This program will provide a better teaching and learning experience-for you and your students. Here's how: Improve Results: MyMathLab® delivers proven results in helping students succeed and provides engaging experiences that personalize learning. Help students prepare for class with just-in-time review for topics ahead. Reinforce key concepts with practicing skills exercises that allow students to practice immediately after learning a new skill. Review for exams and quizzes with comprehensive practice problems matched to learning objectives for each section.  . |
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