CHAPTER P Prerequisites 



2  (11) 

P.2 Cartesian Coordinate System 


13  (10) 

P.3 Linear Equations and Inequalities 


23  (7) 


30  (14) 

P.5 Solving Equations Graphically, Numerically, and Algebraically 


44  (9) 

P.6 Solving Inequalities Algebraically and Graphically 


53  (2) 


55  (2) 


57  (7) 
CHAPTER 1 Functions and Graphs 


1.1 Modeling and Equation Solving 


64  (17) 

1.2 Functions and Their Properties 


81  (20) 

1.3 Twelve Basic Functions 


101  (12) 

1.4 Building Functions from Functions 


113  (18) 

1.5 Graphical Transformations 


131  (11) 

1.6 Modeling with Functions 


142  (14) 


156  (1) 


156  (1) 


157  (13) 


170  
CHAPTER 2 Polynomial, Power, and Rational Functions 


2.1 Linear and Quadratic Functions and Modeling 


162  (19) 

2.2 Power Functions with Modeling 


181  (12) 

2.3 Polynomial Functions of Higher Degree with Modeling 


193  (14) 

2.4 Real Zeros of Polynomial Functions 


207  (14) 


221  (8) 

2.6 Complex Zeros and the Fundamental Theorem of Algebra 


229  (8) 

2.7 Graphs of Rational Functions 


237  (12) 

2.8 Solving Equations in One Variable 


249  (9) 

2.9 Solving Inequalities in One Variable 


258  (10) 


268  (1) 


269  (1) 


270  (4) 


274  (2) 
CHAPTER 3 Exponential, Logistic, and Logarithmic Functions 


3.1 Exponential and Logistic Functions 


276  (14) 

3.2 Exponential and Logistic Modeling 


290  (10) 

3.3 Logarithmic Functions and Their Graphs 


300  (10) 

3.4 Properties of Logarithmic Functions 


310  (10) 

3.5 Equation Solving and Modeling 


320  (14) 

3.6 Mathematics of Finance 


334  (11) 


345  (1) 


346  (4) 


350  (2) 
CHAPTER 4 Trigonometric Functions 


4.1 Angles and Their Measures 


352  (10) 

4.2 Trigonometric Functions of Acute Angles 


362  (10) 

4.3 Trigonometry Extended: The Circular Functions 


372  (14) 

4.4 Graphs of Sine and Cosine: Sinusoids 


386  (12) 

4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant 


398  (9) 

4.6 Graphs of Composite Trigonometric Functions 


407  (9) 

4.7 Inverse Trigonometric Functions 


416  (10) 

4.8 Solving Problems with Trigonometry 


426  (12) 


438  (1) 


439  (3) 


442  (2) 
CHAPTER 5 Analytic Trigonometry 


5.1 Fundamental Identities 


444  (10) 

5.2 Proving Trigonometric Identities 


454  (9) 

5.3 Sum and Difference Identities 


463  (8) 

5.4 MultipleAngle Identities 


471  (7) 


478  (9) 


487  (9) 


496  (1) 


497  (1) 


497  (3) 


500  (2) 
CHAPTER 6 Vectors, Parametric Equations, and Polar Equations 



502  (12) 

6.2 Dot Product of Vectors 


514  (8) 

6.3 Parametric Equations and Motion 


522  (12) 


534  (7) 

6.5 Graphs of Polar Equations 


541  (9) 

6.6 De Moivre's Theorem and nth Roots 


550  (10) 


560  (1) 


561  (3) 


564  (2) 
CHAPTER 7 Systems and Matrices 


7.1 Solving Systems of Two Equations 


566  (11) 


577  (15) 

7.3 Multivariate Linear Systems and Row Operations 


592  (14) 


606  (9) 

7.5 Systems of Inequalities in Two Variables 


615  (8) 


623  (1) 


624  (1) 


624  (4) 


628  (2) 
CHAPTER 8 Analytic Geometry in Two and Three Dimensions 


8.1 Conic Sections and Parabolas 


630  (12) 


642  (12) 


654  (12) 

8.4 Translation and Rotation of Axes 


666  (10) 

8.5 Polar Equations of Conics 


676  (10) 

8.6 ThreeDimensional Cartesian Coordinate System 


686  (11) 


697  (1) 


697  (3) 


700  (2) 
CHAPTER 9 Discrete Mathematics 



702  (11) 


713  (6) 


719  (14) 


733  (17) 

9.5 Mathematical Induction 


750  (8) 

9.6 Statistics and Data (Graphical) 


758  (13) 

9.7 Statistics and Data (Algebraic) 


771  (16) 


787  (1) 


787  (1) 


788  (4) 


792  (2) 
CHAPTER 10 An Introduction to Calculus: Limits, Derivatives, and Integrals 


10.1 Limits and Motion: The Tangent Problem 


794  (12) 

10.2 Limits and Motion: The Area Problem 


806  (9) 


815  (14) 

10.4 Numerical Derivatives and Integrals 


829  (11) 


840  (1) 


840  (2) 


842  (1) 
A.1 Radicals and Rational Exponents 

843  (5) 
A.2 Polynomials and Factoring 

848  (8) 
A.3 Fractional Expressions 

856  (5) 
B.1 Formulas from Algebra 

861  (1) 
B.2 Formulas from Geometry 

862  (1) 
B.3 Formulas from Trigonometry 

863  (1) 
B.4 Formulas from Analytic Geometry 

864  (2) 
B.5 Gallery of Basic Functions 

866  (1) 
C.1 Logic: An Introduction 

867  (6) 
C.2 Conditionals and Biconditionals 

873  (8) 
Glossary 

881  (18) 
Selected Answers 

899  (108) 
Applications Index 

1007  (4) 
Index 

1011  