College Algebra (11th Edition)

Cover Page
Title Page
Copyright Page
Dedication
Contents
Three Distinct Series
The Flagship Series
Preface to the Instructor
Acknowledgments
Get the Most Out of MyLab Math
Resources for Success
Applications Index
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 Equations and Inequalities
	1.1 Linear Equations
		Solve a Linear Equation
		Solve Equations That Lead to Linear Equations
		Solve Problems That Can Be Modeled by Linear Equations
	1.2 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
	1.3 Complex Numbers; Quadratic Equations in the Complex
		Add, Subtract, Multiply, and Divide Complex Numbers
		Solve Quadratic Equations in the Complex Number System
	1.4 Radical Equations; Equations Quadratic in Form;
		Solve Radical Equations
		Solve Equations Quadratic in Form
		Solve Equations by Factoring
	1.5 Solving Inequalities
		Use Interval Notation
		Use Properties of Inequalities
		Solve Inequalities
		Solve Combined Inequalities
	1.6 Equations and Inequalities Involving Absolute Value
		Solve Equations Involving Absolute Value
		Solve Inequalities Involving Absolute Value
	1.7 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
	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 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
	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 an 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
		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 and the 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
	Graphing Polynomial Functions; Models
		Graph a Polynomial Function
		Graph a Polynomial Function Using a Graphing Utility
		Build Cubic Models from Data
	5.3 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
	5.4 The Graph of a Rational Function
		Graph a Rational Function
		Solve Applied Problems Involving Rational Functions
	5.5 Polynomial and Rational Inequalities
		Solve Polynomial Inequalities
		Solve Rational Inequalities
	5.6 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 of Theorem
	5.7 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
	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
		Obtain the Graph of the Inverse Function from the Graph of a One-to-One Function
		Verify 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 10 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;
		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 Analytic Geometry
	7.1 Conics
		Know the Names of the Conics
	7.2 The Parabola
		Analyze Parabolas with Vertex at the Origin
		Analyze Parabolas with Vertex at (h, k)
		Solve Applied Problems Involving Parabolas
	7.3 The Ellipse
		Analyze Ellipses with Center at the Origin
		Analyze Ellipses with Center at (h, k)
		Solve Applied Problems Involving Ellipses
	7.4 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
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
8 Systems of Equations and Inequalities
	8.1 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
	8.2 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
	8.3 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
	8.4 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
	8.5 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
	8.6 Systems of Nonlinear Equations
		Solve a System of Nonlinear Equations Using Substitution
		Solve a System of Nonlinear Equations Using Elimination
	8.7 Systems of Inequalities
		Graph an Inequality
		Graph a System of Inequalities
	8.8 Linear Programming
		Set Up a Linear Programming Problem
		Solve a Linear Programming Problem
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
9 Sequences; Induction; the Binomial Theorem
	9.1 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
	9.2 Arithmetic Sequences
		Determine Whether a Sequence Is Arithmetic
		Find a Formula for an Arithmetic Sequence
		Find the Sum of an Arithmetic Sequence
	9.3 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
	9.4 Mathematical Induction
		Prove Statements Using Mathematical Induction
	9.5 The Binomial Theorem
		Evaluate (n j)
		Use the Binomial Theorem
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
10 Counting and Probability
	10.1 Counting
		Find All the Subsets of a Set
		Count the Number of Elements in a Set
		Solve Counting Problems Using the Multiplication Principle
	10.2 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
	10.3 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
Appendix Graphing Utilities
	A.1 The Viewing Rectangle
	A.2 Using a Graphing Utility to Graph Equations
	A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
	A.4 Using a Graphing Utility to Solve Equations
	A.5 Square Screens
	A.6 Using a Graphing Utility to Graph Inequalities
	A.7 Using a Graphing Utility to Solve Systems of Linear Equations
Additional Instructor Answers
Photo Credits
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