Algebra and Trigonometry Enhanced with Graphing Utilities 8th Edition

✍ Scribed by Michael Sullivan

• Tongue: English
• Leaves: 1248
• Edition: 8
• Category: Library

✦ Table of Contents

Cover
Title Page
Copyright Page
Dedication
Contents
Three Distinct Series
The Enhanced with Graphing Utilities Series
Acknowledgments
Preface to the Instructor
Resources for Success
Applications Index
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D
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To the Student
R Review
R.1 Real Numbers
Work with Sets
Classify Numbers
Evaluate Numerical Expressions
Work with Properties of Real Numbers
R.2 Algebra Essentials
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
Use Scientific Notation
R.3 Geometry Essentials
Use the Pythagorean Theorem and Its Converse
Know Geometry Formulas
Understand Congruent Triangles and Similar Triangles
R.4 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
R.5 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
R.6 Synthetic Division
Divide Polynomials Using Synthetic Division
R.7 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
R.8 nth Roots; Rational Exponents
Work with nth Roots
Simplify Radicals
Rationalize Denominators and Numerators
Simplify Expressions with Rational Exponents
1 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations
Graph Equations by Plotting Points
Graph Equations Using a Graphing Utility
Use a Graphing Utility to Create Tables
Find Intercepts from a Graph
Use a Graphing Utility to Approximate Intercepts
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
Solve Equations Using a Graphing Utility
Solve Linear Equations
Solve Rational Equations
Solve Problems That Can Be Modeled by Linear Equations
1.3 Quadratic Equations
Solve a Quadratic Equation by Factoring
Solve a Quadratic Equation Using the Square Root Method
Solve a Quadratic Equation by Completing the Square
Solve a Quadratic Equation Using the Quadratic Formula
Solve Problems That Can Be Modeled by Quadratic Equations
1.4 Complex Numbers; Quadratic Equations in the Complex Number System
Add, Subtract, Multiply, and Divide Complex Numbers
Solve Quadratic Equations in the Complex Number System
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
Solve Radical Equations
Solve Equations Quadratic in Form
Solve Equations Involving Absolute Value
Solve Equations by Factoring
1.6 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
1.7 Solving Inequalities
Use Interval Notation
Use Properties of Inequalities
Solve Linear Inequalities Algebraically and Graphically
Solve Combined Inequalities Algebraically and Graphically
Solve Absolute Value Inequalities Algebraically and Graphically
Chapter Review
Chapter Test
Chapter Projects
2 Graphs
2.1 The Distance and Midpoint Formulas
Use the Distance Formula
Use the Midpoint Formula
2.2 Intercepts; Symmetry; Graphing Key Equations
Find Intercepts Algebraically 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
2.3 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
2.4 Circles
Write the Standard Form of the Equation of a Circle
Graph a Circle by Hand and by Using a Graphing Utility
Work with the General Form of the Equation of a Circle
2.5 Variation
Construct a Model Using Direct Variation
Construct a Model Using Inverse Variation
Construct a Model Using Joint Variation
Chapter Review
Chapter Test
Cumulative Review
Chapter Project
3 Functions and Their Graphs
3.1 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
3.2 The Graph of a Function
Identify the Graph of a Function
Obtain Information from or about the Graph of a Function
3.3 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
3.4 Library of Functions; Piecewise‐defined Functions
Graph the Functions Listed in the Library of Functions
Analyze a Piecewise-defined Function
3.5 Graphing Techniques: Transformations
Graph Functions Using Vertical and Horizontal Shifts
Graph Functions Using Compressions and Stretches
Graph Functions Using Reflections about the x-Axis or y-Axis
3.6 Mathematical Models: Building Functions
Build and Analyze Functions
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
4 Linear and Quadratic Functions
4.1 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
Build Linear Models from Verbal Descriptions
4.2 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
4.3 Quadratic Functions and Their Properties
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
4.4 Building Quadratic Models from Verbal Descriptions and from Data
Build Quadratic Models from Verbal Descriptions
Build Quadratic Models from Data
4.5 Inequalities Involving Quadratic Functions
Solve Inequalities Involving a Quadratic Function
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
5 Polynomial and Rational Functions
5.1 Polynomial Functions
Identify Polynomial Functions and Their Degree
Graph Polynomial Functions Using Transformations
Identify the Real Zeros of a Polynomial Function and Their Multiplicity
5.2 The Graph of a Polynomial Function; Models
Analyze the Graph of a Polynomial Function
Build Cubic Models from Data
5.3 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
5.4 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
5.5 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
5.6 The Graph of a Rational Function
Analyze the Graph of a Rational Function
Solve Applied Problems Involving Rational Functions
5.7 Polynomial and Rational Inequalities
Solve Polynomial Inequalities Graphically and Algebraically
Solve Rational Inequalities Graphically and Algebraically
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
6 Exponential and Logarithmic Functions
6.1 Composite Functions
Form a Composite Function
Find the Domain of a Composite Function
6.2 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
6.3 Exponential Functions
Evaluate Exponential Functions
Graph Exponential Functions
Define the Number e
Solve Exponential Equations
6.4 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
6.5 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 Nor e
Graph a Logarithmic Function Whose Base Is Neither Nor e
6.6 Logarithmic and Exponential Equations
Solve Logarithmic Equations
Solve Exponential Equations
Solve Logarithmic and Exponential Equations Using a Graphing Utility
6.7 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
6.8 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
6.9 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
7 Trigonometric Functions
7.1 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
7.2 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
7.3 Computing the Values of Trigonometric Functions of Acute Angles
Find the Exact Values of the TrigonometricFunctions of π/4= 45°
Find the Exact Values of the Trigonometric Functionsof 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
7.4 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
7.5 Unit Circle Approach; Properties of 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
7.6 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 y = cos x 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
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
Graph the Tangent Function y = tan x and the Cotangent Function 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
7.8 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
8 Analytic Trigonometry
8.1 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
8.2 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
8.3 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
8.4 Trigonometric Identities
Use Algebra to Simplify Trigonometric Expressions
Establish Identities
8.5 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
8.6 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
8.7 Product‐to‐Sum and Sum‐to‐Product Formulas
Express Products as Sums
Express Sums as Products
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles
Solve Right Triangles
Solve Applied Problems
9.2 The Law of Sines
Solve SAA or ASA Triangles
Solve SSA Triangles
Solve Applied Problems
9.3 The Law of Cosines
Solve SAS Triangles
Solve SSS Triangles
Solve Applied Problems
9.4 Area of a Triangle
Find the Area of SAS Triangles
Find the Area of SSS Triangles
9.5 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
10 Polar Coordinates; Vectors
10.1 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
10.2 Polar Equations and Graphs
Identify and Graph Polar Equations by Converting to Rectangular Equations
Graph Polar Equations Using a Graphing Utility
Test Polar Equations for Symmetry
Graph Polar Equations by Plotting Points
10.3 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
10.4 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
10.5 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
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
11 Analytic Geometry
11.1 Conics
Know the Names of the Conics
11.2 The Parabola
Analyze Parabolas with Vertex at the Origin
Analyze Parabolas with Vertex at
Solve Applied Problems Involving Parabolas
11.3 The Ellipse
Analyze Ellipses with Center at the Origin
Analyze Ellipses with Center at (h, k)
Solve Applied Problems Involving Ellipses
11.4 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
11.5 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
11.6 Polar Equations of Conics
Analyze and Graph Polar Equations of Conics
Convert the Polar Equation of a Conic to a Rectangular Equation
11.7 Plane Curves and Parametric Equations
Graph Parametric Equations by Hand
Graph Parametric Equations Using a Graphing Utility
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
12 Systems of Equations and Inequalities
12.1 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
12.2 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
12.3 Systems of Linear Equations: Determinants
Evaluate by 2 Determinants
Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables
Evaluate by 3 Determinants
Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables
Know Properties of Determinants
12.4 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
12.5 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
12.6 Systems of Nonlinear Equations
Solve a System of Nonlinear Equations Using Substitution
Solve a System of Nonlinear Equations Using Elimination
12.7 Systems of Inequalities
Graph an Inequality by Hand
Graph an Inequality Using a Graphing Utility
Graph a System of Inequalities
12.8 Linear Programming
Set Up a Linear Programming Problem
Solve a Linear Programming Problem
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
13 Sequences; Induction; the Binomial Theorem
13.1 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 Algebraically and Using a Graphing Utility
Solve Annuity and Amortization Problems Using Recursive Formulas
13.2 Arithmetic Sequences
Determine Whether a Sequence Is Arithmetic
Find a Formula for an Arithmetic Sequence
Find the Sum of an Arithmetic Sequence
13.3 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 Using Formulas
13.4 Mathematical Induction
Prove Statements Using Mathematical Induction
13.5 The Binomial Theorem
Evaluate (n j)
Use the Binomial Theorem
Chapter Review
Chapter Test
Cumulative Review
Chapter Projects
14 Counting and Probability
14.1 Counting
Find All the Subsets of a Set
Count the Number of Elements in a Set
Solve Counting Problems Using the Multiplication Principle
14.2 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
14.3 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
Answers
Photo Credits
Subject Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
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P
Q
R
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T
U
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X
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