Algebra and Trigonometry Graphs and Models, 6e Marvin Bittinger, Judith Beecher, David Ellenbogen, Judith Penna ( )

Algebra & Trigonometry Graphs and Models Contents Preface Content Changes to the Sixth Edition Emphasis on Functions Visual Emphasis Making Connections Ongoing Review Break Through to Improving Results Break Thr ...

Algebra & Trigonometry Graphs and Models Contents Preface Content Changes to the Sixth Edition Emphasis on Functions Visual Emphasis Making Connections Ongoing Review Break Through to Improving Results Break Through to Improving Results Break Through to Improving Results To the Student Just-in-Time Review Chapter 1 Graphs, Functions, and Models 1.1 Introduction to Graphing Graphs Solution Solutions of Equations Solution Graphs of Equations Solution Solution Solution The Distance Formula Solution Solution Midpoints of Segments Solution Solution Circles Solution Solution Solution Visualizing the Graph 1.1 Exercise Set Synthesis 1.2 Functions and Graphs Functions Solution Solution Solution Notation for Functions Solution Graphs of Functions Solution Solution Solution Finding Domains of Functions Solution Solution Visualizing Domain and Range Solution Applications of Functions Solution 1.2 Exercise Set Skill Maintenance Synthesis 1.3 Linear Functions, Slope, and Applications Linear Functions Linear Functions Nonlinear Functions The Linear Function f(x)=mx+b and Slope Solution Solution Applications of Slope Solution Solution Solution Slope–Intercept Equations of Lines Solution Solution Graphing f(x)=mx+b Using m and b Solution Applications of Linear Functions Solution Visualizing the Graph 1.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 1.4 Equations of Lines and Modeling Slope–Intercept Equations of Lines Solution Solution Point–Slope Equations of Lines Point–Slope Equation Solution Using the Point–Slope Equation: Using the Slope-Intercept Equation: Parallel Lines Perpendicular Lines Solution Solution Mathematical Models Curve Fitting Solution Linear Regression Solution The Correlation Coefficient 1.4 Exercise Set Skill Maintenance Synthesis 1.5 Linear Equations, Functions, Zeros, and Applications Linear Equations Solution Special Cases Solution Solution Applications Using Linear Models Solution Solution Solution Solution Solution Zeros of Linear Functions 1.5 Exercise Set Skill Maintenance Synthesis 1.6 Solving Linear Inequalities Linear Inequalities Solution Solution Compound Inequalities Solution Solution An Application Solution 1.6 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis Chapter 1 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing 1 Chapter Test Synthesis Chapter 2 More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications Increasing, Decreasing, and Constant Functions Solution Relative Maximum and Minimum Values Solution Applications of Functions Solution Solution Functions Defined Piecewise Solution Solution Solution Solution Solution 2.1 Exercise Set Skill Maintenance Synthesis 2.2 The Algebra of Functions The Algebra of Functions: Sums, Differences, Products, and Quotients Solution Solution Difference Quotients Solution Solution Solution 2.2 Exercise Set Skill Maintenance Synthesis 2.3 The Composition of Functions The Composition of Functions Solution Solution Solution Decomposing a Function as a Composition Solution Solution 2.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 2.4 Symmetry Symmetry Even Functions and Odd Functions 2.4 Exercise Set Skill Maintenance Synthesis 2.5 Transformations Transformations of Functions Vertical Translations and Horizontal Translations Solution Reflections Solution Vertical and Horizontal Stretchings and Shrinkings Solution Solution Visualizing the Graph 2.5 Exercise Set Skill Maintenance Synthesis 2.6 Variation and Applications Direct Variation Solution Solution Inverse Variation Solution Solution Combined Variation Solution Solution Solution Solution 2.6 Exercise Set Skill Maintenance Vocabulary Review Synthesis Chapter 2 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing 2 Chapter Test Synthesis Chapter 3 Quadratic Functions and Equations; Inequalities 3.1 The Complex Numbers The Complex-Number System Solution Addition and Subtraction Solution Multiplication Solution Solution Conjugates and Division Solution Solution 3.1 Exercise Set Skill Maintenance Synthesis 3.2 Quadratic Equations, Functions, Zeros, and Models Quadratic Equations and Quadratic Functions Solution Completing the Square Solution Solution Using the Quadratic Formula The Discriminant Equations Reducible to Quadratic Solution Applications Solution Solution Solution 3.2 Exercise Set Skill Maintenance Synthesis 3.3 Analyzing Graphs of Quadratic Functions Graphing Quadratic Functions of the Type f(x)=a(x−h)2+k Exploring with Technology Graphing Quadratic Functions of the Type f(x)=ax2+bx+c,a≠0 Solution Solution Solution Solution Applications Solution Solution Solution Visualizing the Graph 3.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review 3.4 Solving Rational Equations and Radical Equations Rational Equations Solution Solution Radical Equations Solution 3.4 Exercise Set Skill Maintenance Synthesis 3.5 Solving Equations and Inequalities with Absolute Value Equations with Absolute Value Solution Inequalities with Absolute Value Solution Solution 3.5 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis Chapter 3 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing 3 Chapter Test Synthesis Chapter 4 Polynomial Functions and Rational Functions 4.1 Polynomial Functions and Modeling The Leading-Term Test Even Degree Odd Degree Solution Finding Zeros of Factored Polynomial Functions Solution Solution Solution Solution Solution Finding Real Zeros on a Calculator Solution Polynomial Models Solution Solution 4.1 Exercise Set Skill Maintenance Synthesis 4.2 Graphing Polynomial Functions Graphing Polynomial Functions Solution Solution Solution The Intermediate Value Theorem Solution Visualizing the Graph 4.2 Exercise Set Skill Maintenance 4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem Division and Factors Solution The Remainder Theorem and Synthetic Division Proof (Optional). Solution Solution Solution Solution Finding Factors of Polynomials Proof (Optional). Solution 4.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 4.4 Theorems about Zeros of Polynomial Functions The Fundamental Theorem of Algebra Finding Polynomials with Given Zeros Solution Solution Zeros of Polynomial Functions with Real Coefficients Rational Coefficients Solution Solution Integer Coefficients and the Rational Zeros Theorem Solution Solution Descartes’ Rule of Signs Solution Solution Solution Solution 4.4 Exercise Set Skill Maintenance Synthesis 4.5 Rational Functions The Domain of a Rational Function Solution Solution Asymptotes Vertical Asymptotes Solution Horizontal Asymptotes Solution Solution Solution Oblique Asymptotes Solution Solution Solution Solution Solution Applications Solution Visualizing the Graph 4.5 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis 4.6 Polynomial Inequalities and Rational Inequalities Polynomial Inequalities Solution Solution Solution Solution Rational Inequalities Solution Solution Solution 4.6 Exercise Set Skill Maintenance Synthesis Chapter 4 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing 4 Chapter Test Synthesis Chapter 5 Exponential Functions and Logarithmic Functions 5.1 Inverse Functions Inverses Solution Solution Inverses and One-to-One Functions Finding Formulas for Inverses Solution Solution Solution Inverse Functions and Composition Solution Restricting a Domain 5.1 Exercise Set Skill Maintenance Synthesis 5.2 Exponential Functions and Graphs Graphing Exponential Functions Solution Solution Solution Applications Solution The Number e Solution Graphs of Exponential Functions, Base e Solution Solution 5.2 Exercise Set Skill Maintenance Synthesis 5.3 Logarithmic Functions and Graphs Logarithmic Functions Solution Finding Certain Logarithms Solution Converting Between Exponential Equations and Logarithmic Equations Solution Solution Finding Logarithms on a Calculator Natural Logarithms Changing Logarithmic Bases Solution Solution Graphs of Logarithmic Functions Solution Solution Solution Applications Solution Solution Visualizing the Graph 5.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review 5.4 Properties of Logarithmic Functions Logarithms of Products Solution Solution A Proof of the Product Rule: Logarithms of Powers Solution A Proof of the Power Rule: Logarithms of Quotients Solution Solution A Proof of the Quotient Rule: Applying the Properties Solution Solution Solution Solution Simplifying Expressions of the Type logaa x and aloga x Solution Solution A Proof of the Change-of-Base Formula: 5.4 Exercise Set Skill Maintenance Synthesis 5.5 Solving Exponential Equations and Logarithmic Equations Solving Exponential Equations Solving Logarithmic Equations Graphical Solution 5.5 Exercise Set Skill Maintenance Synthesis 5.6 Applications and Models: Growth and Decay; Compound Interest Population Growth Solution Interest Compounded Continuously Solution Solution Models of Limited Growth Solution Exponential Decay Solution Exponential and Logarithmic Curve Fitting Solution 5.6 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis Chapter 5 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing 5 Chapter Test Synthesis Chapter 6 The Trigonometric Functions 6.1 Trigonometric Functions of Acute Angles The Trigonometric Ratios Solution Solution Solution The Six Related Functions Solution Function Values of 30°, 45°, and 60° Solution Function Values of Any Acute Angle Solution Solution Solution Solution Solution Cofunctions and Complements Solution 6.1 Exercise Set Skill Maintenance Synthesis 6.2 Applications of Right Triangles Solving Right Triangles Solution Solution Applications Solution Solution Solution Solution Bearing: First-Type Solution Solution 6.2 Exercise Set Skill Maintenance Synthesis 6.3 Trigonometric Functions of Any Angle Angles, Rotations, and Degree Measure Solution Solution Trigonometric Functions of Angles or Rotations Solution The Six Related Functions Solution Terminal Side on an Axis Solution Solution Reference Angles: 30°, 45°, and 60° Solution Function Values for Any Angle Solution Solution Bearing: Second-Type Solution 6.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 6.4 Radians, Arc Length, and Angular Speed Distances on the Unit Circle Solution Solution Radian Measure Solution Solution Solution Solution Arc Length and Central Angles Solution Solution Linear Speed and Angular Speed Solution Solution Solution Solution 6.4 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis 6.5 Circular Functions: Graphs and Properties Reflections on the Unit Circle Solution Finding Function Values Solution Solution Graphs of the Sine and Cosine Functions Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 6.5 Exercise Set Skill Maintenance Synthesis 6.6 Graphs of Transformed Sine Functions and Cosine Functions Variations of Basic Graphs The Constant D Solution The Constant A Solution Solution The Constant B Solution The Constant C Solution Solution Solution Solution Graphs of Sums: Addition of Ordinates Solution Solution Damped Oscillation: Multiplication of Ordinates Solution Visualizing the Graph 6.6 Exercise Set Skill Maintenance Synthesis Chapter 6 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing 6 Chapter Test Synthesis 7 Trigonometric Identities, Inverse Functions, and Equations 7.1 Identities: Pythagorean and Sum and Difference Pythagorean Identities Simplifying Trigonometric Expressions Solution Solution Solution Solution Solution Solution Solution Sum and Difference Identities Solution Solution Solution Solution Solution 7.1 Exercise Set Skill Maintenance Synthesis 7.2 Identities: Cofunction, Double-Angle, and Half-Angle Cofunction Identities Solution Solution Double-Angle Identities Solution Solution Half-Angle Identities Solution Solution 7.2 Exercise Set Skill Maintenance Synthesis 7.3 Proving Trigonometric Identities The Logic of Proving Identities Proving Identities Solution Solution Solution Solution Solution Product-to-Sum and Sum-to-Product Identities Solution Solution 7.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 7.4 Inverses of the Trigonometric Functions Restricting Ranges to Define Inverse Functions Solution Solution Composition of Trigonometric Functions and Their Inverses Solution Solution Solution Solution Solution 7.4 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis 7.5 Solving Trigonometric Equations Solution Solution Solution Solution Solution Solution Solution Solution Visualizing the Graph 7.5 Exercise Set Skill Maintenance Synthesis Chapter 7 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing 7 Chapter Test Synthesis Chapter 8 Applications of Trigonometry 8.1 The Law of Sines Solving Oblique Triangles The Law of Sines Solving Triangles (AAS and ASA) Solution Solution Solving Triangles (SSA) Solution Solution Solution The Area of a Triangle Solution 8.1 Exercise Set Skill Maintenance Synthesis 8.2 The Law of Cosines The Law of Cosines Solving Triangles (SAS) Solution Solution Solving Triangles (SSS) Solution Solution Solution 8.2 Exercise Set Skill Maintenance Synthesis 8.3 Complex Numbers: Trigonometric Notation Graphical Representation Solution Solution Trigonometric Notation for Complex Numbers Solution Solution Multiplication and Division with Trigonometric Notation Solution Solution Solution Solution Powers of Complex Numbers Solution Roots of Complex Numbers Solution Solution Solution 8.3 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 8.4 Polar Coordinates and Graphs Polar Coordinates Solution Solution Solution Polar Equations and Rectangular Equations Solution Solution Graphing Polar Equations Solution Solution Solution Visualizing the Graph 8.4 Exercise Set Skill Maintenance Synthesis 8.5 Vectors and Applications Vectors Solution Vector Addition Applications Solution Solution Components Solution Solution 8.5 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis 8.6 Vector Operations Position Vectors Solution Solution Operations on Vectors Solution Solution Unit Vectors Solution Solution Solution Solution Direction Angles Solution Solution Solution Angle Between Vectors Solution Solution Forces in Equilibrium Solution 8.6 Exercise Set Skill Maintenance Synthesis Chapter 8 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing Chapter Test Synthesis Chapter 9 Systems of Equations and Matrices 9.1 Systems of Equations in Two Variables Solving Systems of Equations Graphically Solution The Substitution Method Solution The Elimination Method Solution Solution Applications Solution Solution Solution Visualizing the Graph 9.1 Exercise Set Skill Maintenance Synthesis 9.2 Systems of Equations in Three Variables Solving Systems of Equations in Three Variables Solution Solution Applications Solution Mathematical Models and Applications Solution 9.2 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis 9.3 Matrices and Systems of Equations Matrices and Row-Equivalent Operations Gaussian Elimination with Matrices Solution Solution Gauss–Jordan Elimination Solution Solution 9.3 Exercise Set Skill Maintenance Synthesis 9.4 Matrix Operations Matrix Addition and Subtraction Solution Solution Solution Scalar Multiplication Solution Solution Products of Matrices Solution Solution Matrix Equations Solution 9.4 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 9.5 Inverses of Matrices The Identity Matrix Solution The Inverse of a Matrix Solution Solution Solution Solving Systems of Equations Solution 9.5 Exercise Set Skill Maintenance Synthesis 9.6 Determinants and Cramer’s Rule Determinants of Square Matrices Solution Evaluating Determinants Using Cofactors Solution Solution Solution Solution Cramer’s Rule Solution 9.6 Exercise Set Skill Maintenance Synthesis 9.7 Systems of Inequalities and Linear Programming Graphs of Linear Inequalities Solution Solution Solution Solution Systems of Linear Inequalities Solution Solution Applications: Linear Programming Solution 9.7 Exercise Set Skill Maintenance Synthesis 9.8 Partial Fractions Partial Fraction Decompositions Solution Solution Solution Solution Solution 9.8 Exercise Set Skill Maintenance Synthesis Chapter 9 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing Chapter Test 9 Synthesis Chapter 10 Analytic Geometry Topics 10.1 The Parabola Parabolas Solution Solution Finding Standard Form by Completing the Square Solution Solution Applications Exercise Set 10.1 Skill Maintenance Synthesis 10.2 The Circle and the Ellipse Circles Solution Ellipses Solution Solution Solution Applications Exercise Set 10.2 Skill Maintenance Vocabulary Reinforcement Synthesis 10.3 The Hyperbola Standard Equations of Hyperbolas Solution Solution Solution ❯ Applications Exercise Set 10.3 Skill Maintenance Synthesis 10.4 Nonlinear Systems of Equations and Inequalities Nonlinear Systems of Equations ❯ Modeling and Problem Solving Solution Nonlinear Systems of Inequalities Solution Solution Visualizing the Graph Exercise Set 10.4 Skill Maintenance Synthesis Mid-Chapter Mixed Review Collaborative Discussion and Writing 10.5 Rotation of Axes Rotation of Axes Solution Solution ❯ The Discriminant Solution Solution Exercise Set 10.5 Skill Maintenance Synthesis 10.6 Polar Equations of Conics ❯ Polar Equations of Conics Solution Solution Solution ❯ Converting from Polar Equations to Rectangular Equations Solution Finding Polar Equations of Conics Solution Exercise Set 10.6 Skill Maintenance Synthesis 10.7 Parametric Equations Graphing Parametric Equations Solution Determining a Rectangular Equation for Given Parametric Equations Solution Solution Solution Solution Determining Parametric Equations for a Given Rectangular Equation Solution Applications Solution Solution Exercise Set 10.7 Skill Maintenance Synthesis Chapter 10 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing Chapter Test 10 Synthesis Chapter 11 Sequences, Series, and Combinatorics 11.1 Sequences and Series Solution Solution Solution Finding the General Term Solution Sums and Series Solution Solution Sigma Notation Solution Solution Recursive Definitions Solution 11.1 Exercise Set Skill Maintenance Synthesis 11.2 Arithmetic Sequences and Series Arithmetic Sequences Solution Solution Solution Solution Sum of the First n Terms of an Arithmetic Sequence Solution Solution Solution Applications Solution Solution 11.2 Exercise Set Skill Maintenance Synthesis 11.3 Geometric Sequences and Series Geometric Sequences Solution Solution Solution Sum of the First n Terms of a Geometric Sequence Solution Solution Infinite Geometric Series Solution Solution Applications Solution Solution Solution Visualizing the Graph 11.3 Exercise Set Skill Maintenance Synthesis 11.4 Mathematical Induction Proving Infinite Sequences of Statements Proof. Proof. Proof. 11.4 Exercise Set Skill Maintenance Synthesis Mid-Chapter Mixed Review 11.5 Combinatorics: Permutations Permutations Solution Solution Solution Solution Factorial Notation Solution Permutations of n Objects Taken k at a Time Solution Solution Solution Solution Permutations of Sets with Nondistinguishable Objects Solution 11.5 Exercise Set Skill Maintenance Synthesis 11.6 Combinatorics: Combinations Combinations Solution Solution Solution Solution Solution 11.6 Exercise Set Skill Maintenance Synthesis 11.7 The Binomial Theorem Binomial Expansion Using Pascal’s Triangle Solution Solution Binomial Expansion Using Combination Notation Solution Solution Finding a Specific Term Solution Solution Total Number of Subsets Solution Solution 11.7Exercise Set Skill Maintenance Synthesis 11.8 Probability Experimental Probability and Theoretical Probability Computing Experimental Probabilities Solution Solution Theoretical Probability Solution Solution Solution Solution Solution Solution Solution Solution 11.8 Exercise Set Skill Maintenance Vocabulary Reinforcement Synthesis Chapter 11 Summary and Review Study Guide Review Exercises Synthesis Collaborative Discussion and Writing Chapter Test 11 Synthesis Answers Chapter 1 Visualizing the Graph Exercise Set 1.1 Exercise Set 1.2 Visualizing the Graph Exercise Set 1.3 Mid-Chapter Mixed Review: Chapter 1 Exercise Set 1.4 Exercise Set 1.5 Exercise Set 1.6 Review Exercises: Chapter 1 Test: Chapter 1 Chapter 2 Exercise Set 2.1 Exercise Set 2.2 Exercise Set 2.3 Mid-Chapter Mixed Review: Chapter 2 Exercise Set 2.4 Visualizing the Graph Exercise Set 2.5 Exercise Set 2.6 Review Exercises: Chapter 2 Test: Chapter 2 Chapter 3 Exercise Set 3.1 Exercise Set 3.2 Visualizing the Graph Exercise Set 3.3 Mid-Chapter Mixed Review: Chapter 3 Exercise Set 3.4 Exercise Set 3.5 Review Exercises: Chapter 3 Test: Chapter 3 Chapter 4 Exercise Set 4.1 Visualizing the Graph Exercise Set 4.2 Exercise Set 4.3 Mid-Chapter Mixed Review: Chapter 4 Exercise Set 4.4 Visualizing the Graph Exercise Set 4.5 Exercise Set 4.6 Review Exercises: Chapter 4 Test: Chapter 4 Chapter 5 Exercise Set 5.1 Exercise Set 5.2 Visualizing the Graph Exercise Set 5.3 Mid-Chapter Mixed Review: Chapter 5 Exercise Set 5.4 Exercise Set 5.5 Exercise Set 5.6 Review Exercises: Chapter 5 Test: Chapter 5 Chapter 6 Exercise Set 6.1 Exercise Set 6.2 Exercise Set 6.3 Mid-Chapter Mixed Review: Chapter 6 Exercise Set 6.4 Exercise Set 6.5 Visualizing the Graph Exercise Set 6.6 Review Exercises: Chapter 6 Test: Chapter 6 Chapter 7 Exercise Set 7.1 Exercise Set 7.2 Exercise Set 7.3 Mid-Chapter Mixed Review: Chapter 7 Exercise Set 7.4 Visualizing the Graph Exercise Set 7.5 Review Exercises: Chapter 7 Test: Chapter 7 Chapter 8 Exercise Set 8.1 Exercise Set 8.2 Exercise Set 8.3 Mid-Chapter Mixed Review: Chapter 8 Visualizing the Graph Exercise Set 8.4 Exercise Set 8.5 Exercise Set 8.6 Review Exercises: Chapter 8 Test: Chapter 8 Chapter 9 Visualizing the Graph Exercise Set 9.1 Exercise Set 9.2 Exercise Set 9.3 Exercise Set 9.4 Mid-Chapter Mixed Review: Chapter 9 Exercise Set 9.5 Exercise Set 9.6 Exercise Set 9.7 Exercise Set 9.8 Review Exercises: Chapter 9 Test: Chapter 9 Chapter 10 Exercise Set 10.1 Exercise Set 10.2 Exercise Set 10.3 Visualizing the Graph Exercise Set 10.4 Mid-Chapter Mixed Review: Chapter 10 Exercise Set 10.5 Exercise Set 10.6 Exercise Set 10.7 Review Exercises: Chapter 10 Test: Chapter 10 Chapter 11 Exercise Set 11.1 Exercise Set 11.2 Visualizing the Graph Exercise Set 11.3 Exercise Set 11.4 Mid-Chapter Mixed Review: Chapter 11 Exercise Set 11.5 Exercise Set 11.6 Exercise Set 11.7 Exercise Set 11.8 Review Exercises: Chapter 11 Test: Chapter 11 Just-in-Time 1. Real Numbers 2. Properties of Real Numbers 3. Order on the Number Line 4. Absolute Value 5. Operations with Real Numbers 6. Interval Notation 7. Integers as Exponents 8. Scientific Notation 9. Order of Operations 10. Introduction to Polynomials 11. Add and Subtract Polynomials 12. Multiply Polynomials 13. Special Products of Binomials 14. Factor Polynomials; The FOIL Method 15. Factor Polynomials: The ac-Method 16. Special Factorizations 17. Equation-Solving Principles 18. Inequality-Solving Principles 19. The Principle of Zero Products 20. The Principle of Square Roots 21. Simplify Rational Expressions 22. Multiply and Divide Rational Expressions 23. Add and Subtract Rational Expressions 24. Simplify Complex Rational Expressions 25. Simplify Radical Expressions 26. Rationalize Denominators 27. Rational Exponents 28. The Pythagorean Theorem Index A B C D E F G H I J L M N O P Q R S T U V W X Y Z Index of Applications Agriculture Astronomy Automotive Biology/Life Sciences Business Chemistry Construction Consumer Economics Education Engineering Environment Finance General Interest Geometry Government Health/Medicine Labor Physics Social Sciences Sports/Entertainment Statistics/Demographics Transportation Photo Credits Chapter 1: Chapter 2: Chapter 3: Chapter 4: Chapter 5: Chapter 6: Chapter 7: Chapter 8: Chapter 9: Chapter 10: Chapter 11: Geometry Special-Product Formulas Factoring Formulas Interval Notation Absolute Value Equation-Solving Principles Inequality-Solving Principles The Distance Formula The Midpoint Formula Formulas Involving Lines The Quadratic Formula Compound Interest Formulas Properties of Exponential and Logarithmic Functions Conic Sections Arithmetic Sequences and Series Geometric Sequences and Series Trigonometry