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ویرایش: 5
نویسندگان: Michael Sullivan. Michael Sullivan
سری:
ISBN (شابک) : 0137978081, 9780137978083
ناشر: Pearson
سال نشر: 2023
تعداد صفحات: 1274
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 77 مگابایت
در صورت تبدیل فایل کتاب Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب پیش حساب: مفاهیم از طریق توابع، رویکرد مثلث قائم الزاویه به مثلثات نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
Cover Title Page Copyright Page Dedication Contents To the Student The Concepts Through Functions Series Preface to the Instructor Pearson’s Commitment to Diversity, Equity, and Inclusion Acknowledgments 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 with Respect to the x-Axis, the y-Axis, and the Origin Know How to Graph Key Equations F.3 Lines Calculate and Interpret the Slope of a Line Graph Lines Given a Point and the Slope Find the Equation of a Vertical Line Use the Point–Slope Form of a Line Identify Horizontal Lines Use the Slope-Intercept Form of a Line Find the Equation of a Line Given Two Points 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 Describe a Relation Determine Whether a Relation Represents a Function Use Function Notation Find the Value of a Function Find the Difference Quotient of a Function Find the Domain of a Function Defined by an Equation Form the Sum, Difference, Product, and Quotient of Two Functions 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 Identify Even and Odd Functions from a Graph Identify Even and Odd Functions from an 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 Analyze a Piecewise-defined Function 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 Building Mathematical Models from Verbal Descriptions Build and Analyze Functions 1.7 Building Mathematical Models Using Variation Construct a Model Using Direct Variation Construct a Model Using Inverse Variation Construct a Model Using Joint Variation 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 Plots 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 Vertex and Axis of Symmetry of a Parabola 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 Test Cumulative Review Chapter Projects 3 Polynomial andRational Functions 3.1 Polynomial Functions Identify Polynomial Functions and Their Degree Graph Polynomial Functions Using Transformations Identify the Real Zeros of a Polynomial Function and Their Multiplicity 3.2 Graphing Polynomial Functions; Models Graph a Polynomial Function Graph a Polynomial Function Using a Graphing Utility Build Cubic Models from Data 3.3 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 Real Zeros of a Polynomial Function Solve Polynomial Equations Use the Theorem for Bounds on Zeros Use the Intermediate Value Theorem 3.4 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 3.5 Properties of Rational Functions Find the Domain of a Rational Function Find the Vertical Asymptotes of a Rational Function Find a Horizontal or an Oblique Asymptote of a Rational Function 3.6 The Graph of a Rational Function Graph a Rational Function Solve Applied Problems Involving Rational Functions 3.7 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 Mapping or a Set of Ordered Pairs Obtain the Graph of the Inverse Function from the Graph of a One-to-One Function Verify that a Function Defined by an Equation Is an Inverse 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 the Properties of Logarithms Write a Logarithmic Expression as a Sum or Difference of Logarithms Write a Logarithmic Expression as a Single Logarithm Evaluate Logarithms 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 Model Populations That Obey the Law of Uninhibited Growth Model Populations That Obey the Law of Uninhibited 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, Arc Length, and Circular Motion Angles and Degree Measure Convert Between Decimal and Degree, Minute, Second Measures for Angles Find the Length of an Arc of a Circle Convert from Degrees to 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 Right Triangle Trigonometry Find the Values of Trigonometric Functions of Acute Angles Use Fundamental Identities Find the Values of the Remaining Trigonometric Functions, Given the Value of One of Them Use the Complementary Angle Theorem 5.3 Computing the Values of TrigonometricFunctions of Acute Angles Find the Exact Values of the Trigonometric Functions of π/4 = 45° Find the Exact Values of the Trigonometric Functions of π/6 = 30° and π/3 = 60° Use a Calculator to Approximate the Values of the Trigonometric Functions of Acute Angles Model and Solve Applied Problems Involving Right Triangles 5.4 Trigonometric Functions of Any Angle Find the Exact Values of the Trigonometric Functions for Any Angle Use Coterminal Angles to Find the Exact Value of a Trigonometric Function Determine the Signs of the Trigonometric Functions of an Angle in a Given Quadrant Find the Reference Angle of an Angle Use a Reference Angle to Find the Exact Value of a Trigonometric Function Find the Exact Values of the Trigonometric Functions of an Angle, Given Information about the Functions 5.5 Unit Circle Approach; Propertiesof the Trigonometric Functions Find the Exact Values of the Trigonometric Functions Using the Unit Circle Know the Domain and Range of the Trigonometric Functions Use Periodic Properties to Find the Exact Values of the Trigonometric Functions Use Even–Odd Properties to Find the Exact Values of the Trigonometric Functions 5.6 Graphs of the Sine and Cosine Functions Graph the Sine Function y = sin x and Functions of the Form y = A sin (ωx) Graph the Cosine Function and Functions of the Form y = A cos (ωx) Determine the Amplitude and Period of Sinusoidal Functions Graph Sinusoidal Functions Using Key Points Find an Equation for a Sinusoidal Graph 5.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions Graph the Tangent Function y = tan x and the CotangentFunction y = cot x Graph Functions of the Form y = A tan (ωx) + B and y = A cot (ωx) + B Graph the Cosecant Function y = csc x and the Secant Function y = sec x Graph Functions of the Form y = A csc (ωx) + B and y = A sec(ωx) + B 5.8 Phase Shift; Sinusoidal Curve Fitting Graph Sinusoidal Functions of the Form y = A sin (ωx − φ) + B Build Sinusoidal Models from Data Chapter Review Chapter Test Cumulative Review Chapter Projects 6 Analytic Trigonometry 6.1 The Inverse Sine, Cosine, and Tangent Functions Define the Inverse Sine Function Find the Value of an Inverse Sine Function Define the Inverse Cosine Function Find the Value of an Inverse Cosine Function Define the Inverse Tangent Function Find the Value of an Inverse Tangent Function Use Properties of Inverse Functions to Find Exact Values of Certain Composite Functions Find the Inverse Function of a Trigonometric Function Solve Equations Involving Inverse Trigonometric Functions 6.2 The Inverse Trigonometric Functions (Continued) Define the Inverse Secant, Cosecant, and Cotangent Functions Find the Value of Inverse Secant, Cosecant, and Cotangent Functions Find the Exact Value of Composite Functions Involving the Inverse Trigonometric Functions Write a Trigonometric Expression as an Algebraic Expression 6.3 Trigonometric Equations Solve Equations Involving a Single Trigonometric Function Solve Trigonometric Equations Using a Calculator Solve Trigonometric Equations Quadratic in Form Solve Trigonometric Equations Using Fundamental Identities Solve Trigonometric Equations Using a Graphing Utility 6.4 Trigonometric Identities Use Algebra to Simplify Trigonometric Expressions Establish Identities 6.5 Sum and Difference Formulas Use Sum and Difference Formulas to Find Exact Values Use Sum and Difference Formulas to Establish Identities Use Sum and Difference Formulas Involving Inverse Trigonometric Functions Solve Trigonometric Equations Linear in Sine and Cosine 6.6 Double-angle and Half-angle Formulas Use Double-angle Formulas to Find Exact Values Use Double-angle Formulas to Establish Identities Use Half-angle Formulas to Find Exact Values 6.7 Product-to-Sum and Sum-to-Product Formulas Express Products as Sums Express Sums as Products Chapter Review Chapter Test Cumulative Review Chapter Projects 7 Applications of Trigonometric Functions 7.1 Applications Involving Right Triangles Solve Right Triangles Solve Applied Problems 7.2 The Law of Sines Solve SAA or ASA Triangles Solve SSA Triangles Solve Applied Problems 7.3 The Law of Cosines Solve SAS Triangles Solve SSS Triangles Solve Applied Problems 7.4 Area of a Triangle Find the Area of SAS Triangles Find the Area of SSS Triangles 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves Build a Model for an Object in Simple Harmonic Motion Analyze Simple Harmonic Motion Analyze an Object in Damped Motion Graph the Sum of Two Functions Chapter Review Chapter Test Cumulative Review Chapter Projects 8 Polar Coordinates Vectors 8.1 Polar Coordinates Plot Points Using Polar Coordinates Convert from Polar Coordinates to Rectangular Coordinates Convert from Rectangular Coordinates to Polar Coordinates Transform Equations Between Polar and Rectangular Forms 8.2 Polar Equations and Graphs Identify and Graph Polar Equations by Converting to Rectangular Equations Test Polar Equations for Symmetry Graph Polar Equations by Plotting Points 8.3 The Complex Plane; De Moivre’s Theorem Plot Points in the Complex Plane Convert a Complex Number Between Rectangular Form and Polar Form or Exponential Form Find Products and Quotients of Complex Numbers Use De Moivre’s Theorem Find Complex Roots 8.4 Vectors Graph Vectors Find a Position Vector Add and Subtract Vectors Algebraically Find a Scalar Multiple and the Magnitude of a Vector Find a Unit Vector Find a Vector from Its Direction and Magnitude Model with Vectors 8.5 The Dot Product Find the Dot Product of Two Vectors Find the Angle Between Two Vectors Determine Whether Two Vectors Are Parallel Determine Whether Two Vectors Are Orthogonal Decompose a Vector into Two Orthogonal Vectors Compute Work 8.6 Vectors in Space Find the Distance Between Two Points in Space Find Position Vectors in Space Perform Operations on Vectors Find the Dot Product Find the Angle Between Two Vectors Find the Direction Angles of a Vector 8.7 The Cross Product Find the Cross Product of Two Vectors Know Algebraic Properties of the Cross Product Know Geometric Properties of the Cross Product Find a Vector Orthogonal to Two Given Vectors Find the Area of a Parallelogram Chapter Review Chapter Test Cumulative Review Chapter Projects 9 Analytic Geometry 9.1 Conics Know the Names of the Conics 9.2 The Parabola Analyze Parabolas with Vertex at the Origin Analyze Parabolas with Vertex at (h, k) Solve Applied Problems Involving Parabolas 9.3 The Ellipse Analyze Ellipses with Center at the Origin Analyze Ellipses with Center at (h, k) Solve Applied Problems Involving Ellipses 9.4 The Hyperbola Analyze Hyperbolas with Center at the Origin Find the Asymptotes of a Hyperbola Analyze Hyperbolas with Center at (h, k) Solve Applied Problems Involving Hyperbolas 9.5 Rotation of Axes; General Form of a Conic Identify a Conic Use a Rotation of Axes to Transform Equations Analyze an Equation Using a Rotation of Axes Identify Conics Without Rotating the Axes 9.6 Polar Equations of Conics Analyze and Graph Polar Equations of Conics Convert the Polar Equation of a Conic to a Rectangular Equation 9.7 Plane Curves and Parametric Equations Graph Parametric Equations Find a Rectangular Equation for a Plane Curve Defined Parametrically Use Time as a Parameter in Parametric Equations Find Parametric Equations for Plane Curves Defined by Rectangular Equations Chapter Review Chapter Test Cumulative Review Chapter Projects 10 Systems of Equations and Inequalities 10.1 Systems of Linear Equations: Substitution and Elimination Solve Systems of Equations by Substitution Solve Systems of Equations by Elimination Identify Inconsistent Systems of Equations Containing Two Variables Express the Solution of a System of Dependent Equations Containing Two Variables Solve Systems of Three Equations Containing Three Variables Identify Inconsistent Systems of Equations Containing Three Variables Express the Solution of a System of Dependent Equations Containing Three Variables 10.2 Systems of Linear Equations: Matrices Write the Augmented Matrix of a System of Linear Equations Write the System of Equations from the Augmented Matrix Perform Row Operations on a Matrix Solve a System of Linear Equations Using Matrices 10.3 Systems of Linear Equations: Determinants Evaluate 2 by 2 Determinants Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables Evaluate 3 by 3 Determinants Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables Know Properties of Determinants 10.4 Matrix Algebra Find the Sum and Difference of Two Matrices Find Scalar Multiples of a Matrix Find the Product of Two Matrices Find the Inverse of a Matrix Solve a System of Linear Equations Using an Inverse Matrix 10.5 Partial Fraction Decomposition Decompose P/Q Where Q Has Only Nonrepeated Linear Factors Decompose P/Q Where Q Has Repeated Linear Factors Decompose P/Q Where Q Has a Nonrepeated Irreducible Quadratic Factor Decompose P/Q Where Q Has a Repeated Irreducible Quadratic Factor 10.6 Systems of Nonlinear Equations Solve a System of Nonlinear Equations Using Substitution Solve a System of Nonlinear Equations Using Elimination 10.7 Systems of Inequalities Graph an Inequality Graph a System of Inequalities 10.8 Linear Programming Set Up a Linear Programming Problem Solve a Linear Programming Problem Chapter Review Chapter Test Cumulative Review Chapter Projects 11 Sequences Induction the Binomial Theorem 11.1 Sequences List the First Several Terms of a Sequence List the Terms of a Sequence Defined by a Recursive Formula Use Summation Notation Find the Sum of a Sequence 11.2 Arithmetic Sequences Determine Whether a Sequence Is Arithmetic Find a Formula for an Arithmetic Sequence Find the Sum of an Arithmetic Sequence 11.3 Geometric Sequences; Geometric Series Determine Whether a Sequence Is Geometric Find a Formula for a Geometric Sequence Find the Sum of a Geometric Sequence Determine Whether a Geometric Series Converges or Diverges Solve Annuity Problems 11.4 Mathematical Induction Prove Statements Using Mathematical Induction 11.5 The Binomial Theorem Evaluate (n j) Use the Binomial Theorem Chapter Review Chapter Test Cumulative Review Chapter Projects 12 Counting and Probability 12.1 Counting Find All the Subsets of a Set Count the Number of Elements in a Set Solve Counting Problems Using the Multiplication Principle 12.2 Permutations and Combinations Solve Counting Problems Using Permutations Involving n Distinct Objects Solve Counting Problems Using Combinations Solve Counting Problems Using Permutations Involving N Nondistinct Objects 12.3 Probability Construct Probability Models Compute Probabilities of Equally Likely Outcomes Find Probabilities of the Union of Two Events Use the Complement Rule to Find Probabilities Chapter Review Chapter Test Cumulative Review Chapter Projects 13 A Preview of Calculus: The Limit, Derivative, and Integral of a Function 13.1 Investigating Limits Using Tables and Graphs Investigate a Limit Using a Table Investigate a Limit Using a Graph 13.2 Algebraic Techniques for Finding Limits Find the Limit of a Sum, a Difference, and a Product Find the Limit of a Polynomial Find the Limit of a Power or a Root Find the Limit of a Quotient Find the Limit of an Average Rate of Change 13.3 One-sided Limits; Continuity Find the One-sided Limits of a Function Determine Whether a Function Is Continuous at a Number 13.4 The Tangent Problem; The Derivative Find an Equation of the Tangent Line to the Graph of a Function Find the Derivative of a Function Find Instantaneous Rates of Change Find the Instantaneous Velocity of an Object 13.5 The Area Problem; The Integral Approximate the Area Under the Graph of a Function Approximate Integrals Using a Graphing Utility Chapter Review Chapter Test Chapter Projects Appendix A Review A.1 Algebra Essentials Work with Sets Graph Inequalities Find Distance on the Real Number Line Evaluate Algebraic Expressions Determine the Domain of a Variable Use the Laws of Exponents Evaluate Square Roots Use a Calculator to Evaluate Exponents A.2 Geometry Essentials Use the Pythagorean Theorem and Its Converse Know Geometry Formulas Understand Congruent Triangles and Similar Triangles A.3 Polynomials Recognize Monomials Recognize Polynomials Add and Subtract Polynomials Multiply Polynomials Know Formulas for Special Products Divide Polynomials Using Long Division Work with Polynomials in Two Variables A.4 Factoring Polynomials Factor the Difference of Two Squares and the Sum and Difference of Two Cubes Factor Perfect Squares Factor a Second-degree Polynomial: x² + Bx + C Factor by Grouping Factor a Second-degree Polynomial: Ax² + Bx + C, A ≠ 1 Complete the Square A.5 Synthetic Division Divide Polynomials Using Synthetic Division A.6 Rational Expressions Reduce a Rational Expression to Lowest Terms Multiply and Divide Rational Expressions Add and Subtract Rational Expressions Use the Least Common Multiple Method Simplify Complex Rational Expressions A.7 nth Roots; Rational Exponents Work with nth Roots Simplify Radicals Rationalize Denominators and Numerators Simplify Expressions with Rational Exponents A.8 Solving Equations Solve Linear Equations Solve Rational Equations Solve Equations by Factoring Solve Radical Equations A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications Translate Verbal Descriptions into Mathematical Expressions Solve Interest Problems Solve Mixture Problems Solve Uniform Motion Problems Solve Constant Rate Job Problems A.10 Interval Notation; Solving Inequalities Use Interval Notation Use Properties of Inequalities Solve Inequalities Solve Combined Inequalities A.11 Complex Numbers Add, Subtract, Multiply, and Divide Complex Numbers Appendix B Graphing Utilities B.1 The Viewing Rectangle B.2 Using a Graphing Utility to Graph Equations B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry B.4 Using a Graphing Utility to Solve Equations B.5 Square Screens B.6 Using a Graphing Utility to Graph Inequalities B.7 Using a Graphing Utility to Solve Systems of Linear Equations B.8 Using a Graphing Utility to Graph a Polar Equation B.9 Using a Graphing Utility to Graph Parametric Equations Answers Chapter F Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Appendix A Appendix B Challenge Problem Solutions Chapter F Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Subject Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Endpapers