

1  (68) 


1  (13) 

Representing Real Numbers 



Order and Interval Notation 



Basic Properties of Algebra 







Cartesian Coordinate System 


14  (10) 



Absolute Value of a Real Number 











Linear Equations and Inequalities 


24  (7) 





Linear Equations in One Variable 



Linear Inequalities in One Variable 




31  (13) 



PointSlope Form Equation of a Line 



SlopeIntercept Form Equation of a Line 



Graphing Linear Equations in Two Variables 



Parallel and Perpendicular Lines 



Applying Linear Equations in Two Variables 



Solving Equations Graphically, Numerically, and Algebraically 


44  (9) 

Solving Equations Graphically 



Solving Quadratic Equations 



Approximating Solutions of Equations Graphically 



Approximating Solutions of Equations Numerically with Tables 



Solving Equations by Finding Intersections 




53  (6) 



Operations with Complex Numbers 



Complex Conjugates and Division 



Complex Solutions of Quadratic Equations 



Solving Inequalities Algebraically and Graphically 


59  (10) 

Solving Absolute Value Inequalities 



Solving Quadratic Inequalities 



Approximating Solutions to Inequalities 






65  (1) 


66  (3) 


69  (100) 

Modeling and Equation Solving 


70  (16) 











Grapher Failure and Hidden Behavior 





Functions and Their Properties 


86  (20) 

Function Definition and Notation 







Increasing and Decreasing Functions 





Local and Absolute Extrema 










106  (11) 





Analyzing Functions Graphically 



Building Functions from Functions 


117  (10) 

Combining Functions Algebraically 





Relations and Implicitly Defined Functions 



Parametric Relations and Inverses 


127  (11) 

Relations Defined Parametrically 



Inverse Relations and Inverse Functions 



Graphical Transformations 


138  (13) 



Vertical and Horizontal Translations 





Vertical and Horizontal Stretches and Shrinks 



Combining Transformations 




151  (18) 





Functions from Verbal Descriptions 






164  (1) 


164  (1) 


165  (3) 


168  (1) 

Polynomial, Power, and Rational Functions 


169  (106) 

Linear and Quadratic Functions and Modeling 


170  (18) 



Linear Functions and Their Graphs 





Linear Correlation and Modeling 



Quadratic Functions and Their Graphs 



Applications of Quadratic Functions 



Power Functions with Modeling 


188  (12) 

Power Functions and Variation 



Monomial Functions and Their Graphs 



Graphs of Power Functions 



Modeling with Power Functions 



Polynomial Functions of Higher Degree with Modeling 


200  (14) 

Graphs of Polynomial Functions 



End Behavior of Polynomial Functions 



Zeros of Polynomial Functions 



Intermediate Value Theorem 





Real Zeros of Polynomial Functions 


214  (14) 

Long Division and the Division Algorithm 



Remainder and Factor Theorems 









Complex Zeros and the Fundamental Theorem of Algebra 


228  (9) 





Factoring with Real Number Coefficients 



Graphs of Rational Functions 


237  (11) 



Transformations of the Reciprocal Function 





Analyzing Graphs of Rational Functions 



Exploring Relative Humidity 



Solving Equations in One Variable 


248  (9) 

Solving Rational Equations 







Solving Inequalities in One Variable 


257  (18) 










267  (1) 


268  (1) 


269  (4) 


273  (2) 

Exponential, Logistic, and Logarithmic Functions 


275  (74) 

Exponential and Logistic Functions 


276  (14) 

Exponential Functions and Their Graphs 





Logistic Functions and Their Graphs 





Exponential and Logistic Modeling 


290  (10) 

Constant Percentage Rate and Exponential Functions 



Exponential Growth and Decay Models 



Using Regression to Model Population 





Logarithmic Functions and Their Graphs 


300  (10) 

Inverses of Exponential Functions 



Common LogarithmsBase 10 



Natural LogarithmsBase e 



Graphs of Logarithmic Functions 



Measuring Sound Using Decibels 



Properties of Logarithmic Functions 


310  (10) 





Graphs of Logarithmic Functions with Base b 





Equation Solving and Modeling 


320  (14) 

Solving Exponential Equations 



Solving Logarithmic Equations 



Orders of Magnitude and Logarithmic Models 





Logarithmic Reexpression 




334  (15) 

Interest Compounded Annually 



Interest Compounded k Times per Year 



Interest Compounded Continuously 







Loans and MortgagesPresent Value 




344  (1) 


344  (4) 


348  (1) 


349  (94) 

Angles and Their Measures 


350  (10) 

The Problem of Angular Measure 







Angular and Linear Motion 



Trigonometric Functions of Acute Angles 


360  (10) 

Right Triangle Trigonometry 





Evaluating Trigonometric Functions with a Calculator 



Common Calculator Errors When Evaluating Trig Functions 



Applications of Right Triangle Trigonometry 



Trigonometry Extended: The Circular Functions 


370  (14) 

Trigonometric Functions of Any Angle 



Trigonometric Functions of Real Numbers 







Graphs of Sine and Cosine: Sinusoids 


384  (12) 

The Basic Waves Revisited 



Sinusoids and Transformations 



Modeling Periodic Behavior with Sinusoids 



Graphs of Tangent, Cotangent, Secant, and Cosecant 


396  (10) 









Graphs of Composite Trigonometric Functions 


406  (8) 

Combining Trigonometric and Algebraic Functions 



Sums and Differences of Sinusoids 





Inverse Trigonometric Functions 


414  (11) 



Inverse Cosine and Tangent Functions 



Composing Trigonometric and Inverse Trigonometric Functions 



Applications of Inverse Trigonometric Functions 



Solving Problems with Trigonometry 


425  (18) 

More Right Triangle Problems 






438  (1) 


439  (3) 


442  (1) 


443  (58) 


444  (10) 



Basic Trigonometric Identities 









Simplifying Trigonometric Expressions 



Solving Trigonometric Equations 



Proving Trigonometric Identities 


454  (9) 





Disproving NonIdentities 





Sum and Difference Identities 


463  (8) 





Sine of a Difference or Sum 



Tangent of a Difference or Sum 



Verifying a Sinusoid Algebraically 



MultipleAngle Identities 


471  (7) 



PowerReducing Identities 





Solving Trigonometric Equations 




478  (9) 

Deriving the Law of Sines 



Solving Triangles (AAS, ASA) 








487  (14) 

Deriving the Law of Cosines 



Solving Triangles (SAS, SSS) 



Triangle Area and Heron's Formula 






496  (1) 


497  (1) 


497  (3) 


500  (1) 

Applications of Trigonometry 


501  (66) 


502  (12) 












514  (8) 





Projecting One Vector onto Another 





Parametric Equations and Motion 


522  (12) 





Eliminating the Parameter 





Simulating Motion with a Grapher 




534  (7) 







Finding Distance Using Polar Coordinates 



Graphs of Polar Equations 


541  (9) 

Polar Curves and Parametric Curves 













De Moivre's Theorem and nth Roots 


550  (17) 



Trigonometric Form of Complex Numbers 



Multiplication and Division of Complex Numbers 



Powers of Complex Numbers 






561  (1) 


562  (3) 


565  (2) 


567  (64) 

Solving Systems of Two Equations 


568  (11) 

The Method of Substitution 



Solving Systems Graphically 



The Method of Elimination 






579  (15) 



Matrix Addition and Subtraction 





Identity and Inverse Matrices 



Determinant of a Square Matrix 





Multivariate Linear Systems and Row Operations 


594  (14) 

Triangular Form for Linear Systems 





Elementary Row Operations and Row Echelon Form 





Solving Systems with Inverse Matrices 






608  (9) 

Partial Fraction Decomposition 



Denominators with Linear Factors 



Denominators with Irreducible Quadratic Factors 





Systems of Inequalities in Two Variables 


617  (14) 








625  (1) 


626  (1) 


626  (4) 


630  (1) 

Analytic Geometry in Two and Three Dimensions 


631  (68) 

Conic Sections and Parabolas 


632  (12) 





Translations of Parabolas 



Reflective Property of a Parabola 




644  (12) 







Reflective Property of an Ellipse 




656  (10) 



Translations of Hyperbolas 





Reflective Property of a Hyperbola 





Translation and Rotation of Axes 


666  (9) 

SecondDegree Equations in Two Variables 



Translating Axes versus Translating Graphs 







Polar Equations of Conics 


675  (10) 



Writing Polar Equations for Conics 



Analyzing Polar Equations of Conics 





ThreeDimensional Cartesian Coordinate System 


685  (14) 

ThreeDimensional Cartesian Coordinates 



Distance and Midpoint Formulas 





Planes and Other Surfaces 








695  (1) 


696  (2) 


698  (1) 


699  (92) 


700  (11) 

Discrete Versus Continuous 



The Importance of Counting 



The Multiplication Principle of Counting 










711  (7) 










718  (14) 

Sample Spaces and Probability Functions 



Determining Probabilities 



Venn Diagrams and Tree Diagrams 








732  (10) 



Limits of Infinite Sequences 



Arithmetic and Geometric Sequences 



Sequences and Graphing Calculators 




742  (10) 



Sums of Arithmetic and Geometric Sequences 





Convergence of Geometric Series 




752  (7) 

The Tower of Hanoi Problem 



Principle of Mathematical Induction 





Statistics and Data (Graphical) 


759  (12) 



Displaying Categorical Data 











Statistics and Data (Algebraic) 


771  (20) 

Parameters and Statistics 









Variance and Standard Deviation 






785  (1) 


786  (1) 


786  (4) 


790  (1) 

An Introduction to Calculus: Limits, Derivatives, and Integrals 


791  (86) 

Limits and Motion: The Tangent Problem 


792  (12) 







The Connection to Tangent Lines 





Limits and Motion: The Area Problem 


804  (9) 

Distance from a Constant Velocity 



Distance from a Changing Velocity 










813  (15) 



Defining a Limit Informally 





Limits of Continuous Functions 



Onesided and Twosided Limits 



Limits Involving Infinity 



Numerical Derivatives and Integrals 


828  (11) 

Derivatives on a Calculator 



Definite Integrals on a Calculator 



Computing a Derivative from Data 



Computing a Definite Integral from Data 




836  (1) 


836  (2) 


838  (1) 

APPENDIX A Algebra Review 



A.1 Radicals and Rational Exponents 


839  (6) 



Simplifying Radical Expressions 



Rationalizing the Denominator 





A.2 Polynomials and Factoring 


845  (7) 

Adding, Subtracting, and Multiplying Polynomials 





Factoring Polynomials Using Special Products 







A.3 Fractional Expressions 


852  (5) 

Domain of an Algebraic Expression 



Reducing Rational Expressions 



Operations with Rational Expressions 



Compound Rational Expressions 





B.1 Formulas from Algebra 


857  (1) 



Radicals and Rational Expressions 















Arithmetic Sequences and Series 



Geometric Sequences and Series 









B.2 Formulas from Geometry 


858  (1) 

























B.3 Formulas from Trigonometry 


859  (1) 











Sum and Difference Identities 







PowerReducing Identities 







Trigonometric Form of a Complex Number 





B.4 Formulas from Analytic Geometry 


860  (2) 







Parabolas with Vertex (h, k) 



Ellipses with Center (h, k) and a > b > 0 



Hyperbolas with Center (h, k) 



B.5 Gallery of Basic Functions 


862  (1) 



C.1 Logic: An Introduction 


863  (6) 





C.2 Conditionals and Biconditionals 


869  (8) 




Glossary 

877  (18) 
Selected Answers 

895  (120) 
Applications Index 

1015  (4) 
Index 

1019  