Preface 

xiii  
Supplements 

xvii  


1  (105) 

Real Numbers and Their Properties 


2  (9) 


2  (2) 

Properties of the Real Numbers 


4  (1) 


5  (1) 


6  (1) 


6  (3) 

Equations Involving Absolute Value 


9  (2) 

Linear and Absolute Value Inequalities 


11  (10) 


11  (1) 


12  (2) 


14  (2) 

Absolute Value Inequalities 


16  (2) 

Modeling with Inequalities 


18  (3) 

Equations and Graphs in Two Variables 


21  (11) 

The Cartesian Coordinate System 


21  (1) 


22  (1) 


23  (1) 


24  (3) 


27  (2) 

Using a Graph to Solve an Equation 


29  (3) 

Linear Equations in Two Variables 


32  (11) 


32  (2) 


34  (1) 


35  (1) 

Using Slope to Graph a Line 


36  (1) 

The Three Forms for the Equation of a Line 


37  (1) 


38  (1) 


39  (1) 


40  (3) 


43  (12) 


43  (1) 


44  (3) 


47  (1) 


48  (2) 

The Average Rate of Change of a Function 


50  (2) 


52  (3) 

Graphs of Relations and Functions 


55  (12) 


55  (3) 


58  (1) 


59  (3) 

Increasing, Decreasing, and Constant 


62  (5) 

Families of Functions, Transformations, and Symmetry 


67  (12) 


67  (3) 


70  (2) 


72  (2) 

The Linear Family of Functions 


74  (1) 


74  (5) 

Operations with Functions 


79  (9) 

Basic Operations with Functions 


79  (3) 


82  (3) 


85  (3) 


88  (18) 

OnetoOne and Invertible Functions 


88  (1) 

Determining Whether a Function Is OnetoOne 


89  (2) 

Inverse Functions Using Function Notation 


91  (2) 


93  (1) 

Finding Inverse Functions Mentally 


94  (5) 


99  (2) 

Chapter 1 Review Exercises 


101  (4) 

Concepts of Calculus: Limits 


105  (1) 

Polynomial and Rational Functions 


106  (74) 

Quadratic Functions and Inequalities 


107  (8) 

Two Forms for a Quadratic Function 


107  (2) 

Opening, Vertex, and Axis of Symmetry 


109  (1) 


110  (1) 


111  (2) 

Applications of Maximum and Minimum 


113  (2) 


115  (7) 


115  (2) 

Addition, Subtraction, and Multiplication 


117  (1) 

Division of Complex Numbers 


118  (1) 

Roots of Negative Numbers 


119  (1) 

Imaginary Solutions to Quadratic Equations 


120  (2) 

Zeros of Polynomial Functions 


122  (11) 


122  (1) 


123  (3) 


126  (1) 

The Fundamental Theorem of Algebra 


127  (1) 

The Rational Zero Theorem 


127  (6) 


133  (6) 

The Number of Roots of a Polynomial Equation 


133  (1) 

The Conjugate Pairs Theorem 


134  (1) 


135  (4) 


139  (10) 

Factoring HigherDegree Equations 


139  (1) 

Equations Involving Square Roots 


140  (2) 

Equations with Rational Exponents 


142  (1) 

Equations of Quadratic Type 


143  (2) 

Equations Involving Absolute Value 


145  (4) 

Graphs of Polynomial Functions 


149  (11) 


149  (1) 


149  (2) 

Behavior at the xIntercepts 


151  (1) 

The Leading Coefficient Test 


151  (3) 

Sketching Graphs of Polynomial Functions 


154  (1) 


155  (5) 

Rational Functions and Inequalities 


160  (20) 

Rational Functions and Their Domains 


160  (1) 

Horizontal and Vertical Asymptotes 


161  (2) 


163  (1) 

Sketching Graphs of Rational Functions 


164  (4) 


168  (1) 


169  (5) 


174  (1) 

Chapter 2 Review Exercises 


175  (4) 

Concepts of Calculus: Instantaneous rate of change 


179  (1) 


180  (104) 

Angles and Their Measurements 


181  (10) 


181  (4) 


185  (3) 


188  (3) 

The Sine and Cosine Functions 


191  (8) 


191  (2) 

Sine and Cosine of a Multiple of a 45° 


193  (1) 

Sine and Cosine of a Multiple of a 30° 


194  (1) 

Sine and Cosine of an Arc 


195  (1) 

Approximate Values for Sine and Cosine 


196  (1) 


196  (1) 

Modeling the Motion of a Spring 


197  (2) 

The Graphs of the Sine and Cosine Functions 


199  (14) 


199  (3) 


202  (1) 

Transformations of Sine and Cosine 


203  (2) 


205  (2) 


207  (2) 


209  (4) 

The Other Trigonometric Functions and Their Graphs 


213  (11) 


213  (2) 


215  (2) 


217  (2) 


219  (1) 


220  (4) 

The Inverse Trigonometric Functions 


224  (9) 

The Inverse of the Sine Function 


224  (2) 

The Inverse Cosine Function 


226  (1) 

Inverses of Tangent, Cotangent, Secant, and Cosecant 


227  (3) 

Compositions of Functions 


230  (3) 

Right Triangle Trigonometry 


233  (9) 


233  (1) 


234  (2) 


236  (1) 


237  (5) 


242  (11) 


242  (1) 


243  (1) 

Sum and Difference Identities 


243  (1) 


244  (1) 

DoubleAngle and HalfAngle Identities 


245  (2) 

Product and Sum Identities 


247  (2) 

The Function y = asinx + bcosx 


249  (4) 

Conditional Trigonometric Equations 


253  (11) 


253  (2) 


255  (1) 


256  (1) 

Equations Involving Multiple Angles 


257  (1) 

More Complicated Equations 


258  (3) 

Modeling Projectile Motion 


261  (3) 

The Law of Sines and the Law of Cosines 


264  (20) 


264  (1) 


264  (2) 


266  (3) 


269  (3) 


272  (5) 


277  (2) 

Chapter 3 Review Exercises 


279  (4) 

Concepts of Calculus: Area of a circle and π 


283  (1) 

Exponential and Logarithmic Functions 


284  (44) 

Exponential Functions and Their Applications 


285  (11) 


285  (1) 

Domain of Exponential Functions 


285  (1) 

Graphing Exponential Functions 


286  (3) 

The Exponential Family of Functions 


289  (2) 


291  (1) 

The Compound Interest Model 


291  (2) 

Continuous Compounding and the Number e 


293  (3) 

Logarithmic Functions and Their Applications 


296  (10) 


296  (2) 

Graphs of Logarithmic Functions 


298  (1) 

The Logarithmic Family of Functions 


299  (1) 

Logarithmic and Exponential Equations 


300  (3) 


303  (3) 


306  (8) 

The Product Rule for Logarithms 


306  (1) 

The Quotient Rule for Logarithms 


307  (1) 

The Power Rule for Logarithms 


307  (1) 


308  (1) 


309  (2) 


311  (3) 

More Equations and Applications 


314  (14) 


314  (1) 


315  (2) 

Strategy for Solving Equations 


317  (1) 


317  (2) 

Newton's Model for Cooling 


319  (1) 


320  (3) 


323  (1) 

Chapter 4 Review Exercises 


324  (3) 

Concepts of Calculus: Evaluating transcendental functions 


327  (1) 

Conic Sections, Polar Coordinates, and Parametric Equations 


328  (58) 


329  (9) 


329  (1) 


330  (1) 

The Standard Equation of a Parabola 


331  (1) 


332  (1) 

Parabolas Opening to the Left or Right 


333  (2) 


335  (3) 

The Ellipse and the Circle 


338  (10) 


338  (1) 

The Equation of the Ellipse 


339  (2) 

Graphing an Ellipse Centered at the Origin 


341  (2) 


343  (1) 


344  (1) 


344  (4) 


348  (14) 


349  (1) 


350  (1) 

Graphing a Hyperbola Centered at (0,0) 


351  (4) 

Hyperbolas Centered at (h,k) 


355  (2) 

Finding the Equation of a Hyperbola 


357  (1) 


358  (4) 


362  (10) 


362  (1) 

PolarRectangular Conversions 


363  (1) 


364  (3) 


367  (5) 

Polar Equations of the Conics 


372  (4) 

Alternative Definition of the Conics 


372  (1) 

Polar Equations of the Conics 


372  (2) 

Equivalency of the Definitions 


374  (2) 


376  (10) 

Graphs of Parametric Equations 


376  (1) 

Eliminating the Parameter 


377  (1) 

Writing Parametric Equations 


378  (3) 


381  (1) 

Chapter 5 Review Exercises 


382  (3) 

Concepts of Calculus: The reflection property of a parabola 


385  (1) 

APPENDIX A BASIC ALGEBRA REVIEW 


386  

A.1 Exponents and Radicals 


386  (10) 


386  (1) 

Negative Integral Exponents 


387  (1) 


388  (1) 


389  (1) 


389  (2) 


391  (1) 

The Product and Quotient Rules for Radicals 


392  (1) 

Simplified Form and Rationalizing the Denominator 


393  (1) 

Operations with Radical Expressions 


394  (2) 


396  (6) 


396  (1) 

Naming and Evaluating Polynomials 


397  (1) 

Addition and Subtraction of Polynomials 


397  (1) 

Multiplication of Polynomials 


398  (1) 


399  (1) 


399  (1) 


400  (2) 

A.3 Factoring Polynomials 


402  (5) 

Factoring out the Greatest Common Factor 


402  (1) 


403  (1) 


403  (1) 

Factoring the Special Products 


404  (1) 

Factoring the Difference and Sum of Two Cubes 


405  (1) 


406  (1) 


407  


407  (2) 

Multiplication and Division 


409  (1) 

Building up the Denominator 


410  (1) 


411  
Answers to Selected Exercises 

1  (1) 
Credits 

1  (1) 
Index 

1  