Preface to the Instructor 

x  
Preface to the Student 

xvi  


xxvi  
Photo Credits 

xxxi  


1  (80) 

Rectangular Coordinates; Graphing Utilities 


2  (10) 

Introduction to Graphing Equations 


12  (8) 

Symmetry; Graphing Key Equations; Circles 


20  (13) 


33  (13) 


46  (13) 


59  (22) 


75  (4) 


79  (2) 

Functions and Their Graphs 


81  (92) 


82  (19) 

Linear Functions and Models 


101  (11) 


112  (13) 

Library of Functions; PiecewiseDefined Functions 


125  (10) 

Graphing Techniques: Transformations 


135  (13) 

Operations on Functions; Composite Functions 


148  (10) 

Mathematical Models: Constructing Functions 


158  (15) 


166  (5) 


171  (1) 


172  (1) 

Polynomial and Rational Functions 


173  (100) 

Quadratic Functions and Models 


174  (21) 

Power Functions and Models 


195  (6) 

Polynomial Functions and Models 


201  (13) 


214  (12) 

Rational Functions II: Analyzing Graphs 


226  (10) 

Polynomial and Rational Inequalities 


236  (8) 

The Real Zeros of a Polynomial Function 


244  (15) 

Complex Zeros; Fundamental Theorem of Algebra 


259  (14) 


264  (6) 


270  (1) 


271  (2) 

Exponential and Logarithmic Functions 


273  (94) 

OnetoOne Functions; Inverse Functions 


274  (13) 


287  (14) 


301  (12) 


313  (10) 

Logarithmic and Exponential Equations 


323  (4) 


327  (11) 


338  (11) 

Exponential, Logarithmic, and Logistic Models 


349  (18) 


358  (6) 


364  (1) 


365  (2) 


367  (90) 


368  (14) 

Trigonometric Functions: Unit Circle Approach 


382  (17) 

Properties of the Trigonometric Functions 


399  (15) 

Graphs of the Sine and Cosine Functions 


414  (16) 

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


430  (7) 

Phase Shifts; Sinusoidal Curve Fitting 


437  (20) 


448  (6) 


454  (2) 


456  (1) 


457  (70) 

The Inverse Sine, Cosine, and Tangent Functions 


459  (11) 

The Inverse Trigonometric Functions (continued) 


470  (5) 


475  (7) 

Sum and Difference Formulas 


482  (11) 

DoubleAngle and HalfAngle Formulas 


493  (10) 

ProducttoSum and SumtoProduct Formulas 


503  (4) 

Trigonometric Equations I 


507  (6) 

Trigonometric Equations II 


513  (14) 


520  (4) 


524  (1) 


525  (2) 

Applications of Trigonometric Functions 


527  (54) 

Right Triangle Trigonometry 


528  (11) 


539  (12) 


551  (6) 


557  (6) 

Simple Harmonic Motion; Damped Motion; Combining Waves 


563  (18) 


573  (5) 


578  (2) 


580  (1) 

Polar Coordinates; Vectors 


581  (80) 


582  (9) 

Polar Equations and Graphs 


591  (18) 

The Complex Plane; De Moivre's Theorem 


609  (9) 


618  (12) 


630  (8) 


638  (10) 


648  (13) 


654  (4) 


658  (1) 


659  (2) 


661  (78) 


662  (1) 


663  (12) 


675  (12) 


687  (15) 

Rotation of Axes; General Form of a Conic 


702  (9) 

Polar Equations of Conics 


711  (7) 

Plane Curves and Parametric Equations 


718  (21) 


733  (4) 


737  (1) 


738  (1) 

Systems of Equations and Inequalities 


739  (112) 

Systems of Linear Equations: Two Equations Containing two Variables 


740  (11) 

Systems of Linear Equations: Three Equations Containing Three Variables 


751  (6) 

Systems of Linear Equations: Matrices 


757  (18) 

Systems of Linear Equations: Determinants 


775  (12) 


787  (18) 

Partial Fraction Decomposition 


805  (8) 

Systems of Nonlinear Equations 


813  (11) 


824  (10) 


834  (17) 


842  (6) 


848  (1) 


849  (2) 

Sequences; Induction; The Binomial Theorem 


851  (50) 


852  (15) 


867  (6) 

Geometric Sequences; Geometric Series 


873  (11) 


884  (4) 


888  (13) 


896  (3) 


899  (1) 


900  (1) 


901  (42) 


902  (6) 

Permutations and Combinations 


908  (11) 

Probability of Equally Likely Outcomes 


919  (13) 

Obtaining Probabilities from Data 


932  (11) 


937  (4) 


941  (1) 


942  (1) 

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


943  (44) 

Finding Limits Using Tables and Graphs 


944  (5) 

Algebra Techniques for Finding Limits 


949  (8) 

Onesided Limits; Continuous Functions 


957  (8) 

The Tangent Problem; the Derivative 


965  (8) 

The Area Problem; the Integral 


973  (14) 


981  (4) 


985  (2) 
APPENDIX REVIEW 

987  (1) 


987  (10) 


997  (5) 


1002  (11) 


1013  (9) 

A.5 Polynomial Division; Synthetic Division 


1022  (7) 

A.6 Equations; Completing the Square; the Quadratic Formula 


1029  (8) 

A.7 Complex Numbers; Quadratic Equations with a Negative Discriminant 


1037  (9) 

A.8 Setting Up Equations; Applications 


1046  (14) 

A.9 nth Roots; Rational Exponents 


1060  
Answers 

1  (1) 
Index 

1  