Preface to the Instructor 

xiii  


xix  
Photo Credits 

xxiii  
To the Student 

xxiv  


1  (54) 

Rectangular Coordinates; Graphing Utilities 


2  (9) 

Graphs of Equations in Two Variables 


11  (13) 

Solving Equations in One Variable Using a Graphing Utility 


24  (3) 


27  (17) 


44  (11) 


51  (3) 


54  (1) 


54  (1) 

Functions and Their Graphs 


55  (94) 


56  (15) 


71  (9) 


80  (13) 

Linear Functions and Models 


93  (14) 

Library of Functions; Piecewisedefined Functions 


107  (11) 

Graphing Techniques: Transformations 


118  (12) 

Mathematical Models: Constructing Functions 


130  (19) 


138  (7) 


145  (1) 


146  (1) 


147  (2) 

Polynomial and Rational Functions 


149  (98) 

Quadratic Functions and Models 


150  (20) 

Polynomial Functions and Models 


170  (16) 

Properties of Rational Functions 


186  (12) 

The Graph of a Rational Function; Inverse and Joint Variation 


198  (14) 

Polynomial and Rational Inequalities 


212  (7) 

The Real Zeros of a Polynomial Function 


219  (14) 

Complex Zeros: Fundamental Theorem of Algebra 


233  (14) 


238  (6) 


244  (1) 


245  (1) 


246  (1) 

Exponential and Logarithmic Functions 


247  (108) 


248  (8) 

OnetoOne Functions; Inverse Functions 


256  (15) 


271  (16) 


287  (13) 


300  (9) 

Logarithmic and Exponential Equations 


309  (6) 


315  (9) 

Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay 


324  (13) 

Building Exponential, Logarithmic, and Logistic Models from Data 


337  (18) 


345  (7) 


352  (1) 


353  (1) 


353  (2) 


355  (92) 


356  (14) 

Trigonometric Functions: Unit Circle Approach 


370  (18) 

Properties of the Trigonometric Functions 


388  (14) 

Graphs of the Sine and Cosine Functions 


402  (17) 

Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 


419  (6) 

Phase Shift: Sinusoidal Curve Fitting 


425  (22) 


437  (6) 


443  (2) 


445  (1) 


446  (1) 


447  (70) 

The Inverse Sine, Cosine, and Tangent Functions 


448  (12) 

The Inverse Trigonometric Functions (continued) 


460  (5) 


465  (8) 

Sum and Difference Formulas 


473  (10) 

Doubleangle and Halfangle Formulas 


483  (10) 

ProducttoSum and SumtoProduct Formulas 


493  (3) 

Trigonometric Equations (I) 


496  (7) 

Trigonometric Equations (II) 


503  (14) 


511  (3) 


514  (1) 


515  (1) 


516  (1) 

Applications of Trigonometric Functions 


517  (54) 

Right Triangle Trigonometry; Applications 


518  (13) 


531  (12) 


543  (6) 


549  (6) 

Simple Harmonic Motion; Damped Motion; Combining Waves 


555  (16) 


564  (4) 


568  (1) 


569  (1) 


570  (1) 

Polar Coordinates; Vectors 


571  (80) 


572  (9) 

Polar Equations and Graphs 


581  (19) 

The Complex Plane; De Moivre's Theorem 


600  (8) 


608  (12) 


620  (8) 


628  (10) 


638  (13) 


645  (4) 


649  (1) 


650  (1) 


650  (1) 


651  (74) 


652  (1) 


653  (11) 


664  (11) 


675  (14) 

Rotation of Axes; General Form of a Conic 


689  (9) 

Polar Equations of Conics 


698  (7) 

Plane Curves and Parametric Equations 


705  (20) 


719  (3) 


722  (1) 


723  (1) 


723  (2) 

Systems of Equations and Inequalities 


725  (106) 

Systems of Linear Equations: Substitution and Elimination 


726  (15) 

Systems of Linear Equations: Matrices 


741  (17) 

Systems of Linear Equations: Determinants 


758  (10) 


768  (17) 

Partial Fraction Decomposition 


785  (8) 

Systems of Nonlinear Equations 


793  (11) 


804  (11) 


815  (16) 


823  (5) 


828  (1) 


829  (1) 


830  (1) 

Sequences; Induction; The Binomial Theorem 


831  (44) 


832  (12) 


844  (6) 

Geometric Sequences: Geometric Series 


850  (9) 


859  (4) 


863  (12) 


870  (2) 


872  (1) 


873  (1) 


874  (1) 


875  (34) 


876  (6) 

Permutations and Combinations 


882  (11) 


893  (16) 


904  (3) 


907  (1) 


908  (1) 


908  (1) 

A Preview of Calculus: The Limit, Derivative, and Integral of a Function 


909  (42) 

Finding Limits Using Tables and Graphs 


910  (5) 

Algebra Techniques for Finding Limits 


915  (8) 

Onesided Limits; Continuous Functions 


923  (7) 

The Tangent Problem; The Derivative 


930  (8) 

The Area Problem; The Integral 


938  (13) 


946  (3) 


949  (1) 


950  (1) 


951  


951  (10) 


961  (5) 

A.3. Polynomials and Rational Expressions 


966  (11) 

A.4. Polynomial Division; Synthetic Division 


977  (7) 


984  (16) 

A.6. Complex Numbers; Quadratic Equations in the Complex Number System 


1000  (9) 

A.7. Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs 


1009  (11) 

A.8. Interval Notation; Solving Inequalities 


1020  (12) 

A.9. nth Roots; Rational Exponents; Radical Equations 


1032  
Answers 

1  (1) 
Index 

1  