Preface 

vii  
To the Student 

xi  
Applications Index 

xviii  

Prerequisites: Fundamental Concepts of Algebra 


1  (84) 

Real Numbers and Algebraic Expressions 


2  (11) 

Exponents and Scientific Notation 


13  (10) 

Radicals and Rational Exponents 


23  (12) 


35  (11) 


46  (8) 


54  (11) 


65  (6) 

Graphs and Graphing Utilities 


71  (14) 


81  (1) 

Review Exercises or Algebra Skills Diagnostic Test 


82  (2) 


84  (1) 

Equations, Inequalities, and Mathematical Models 


85  (82) 


86  (11) 

Formulas and Applications 


97  (12) 


109  (18) 


127  (12) 


139  (12) 

Quadratic and Rational Inequalities 


151  (16) 


162  (1) 


163  (2) 


165  (2) 


167  (91) 


168  (12) 

Parallel and Perpendicular Lines and Circles 


180  (10) 

Introduction to Functions 


190  (13) 


203  (18) 

Transformations and Combinations of Functions 


221  (17) 

Composite and Inverse Functions 


238  (20) 


250  (1) 


251  (4) 


255  (1) 

Cumulative Review Exercises 


256  (2) 

Polynomial and Rational Functions 


258  (92) 


259  (13) 

Polynomial Functions and Their Graphs 


272  (1) 

Dividing Polynomials: Remainder and Factor Theorems 


273  (21) 

Zeros of Polynomial Functions 


294  (10) 

More on Zeros of Polynomial Functions 


304  (10) 

Rational Functions and Their Graphs 


314  (18) 


332  (18) 


344  (1) 


345  (3) 


348  (1) 

Cumulative Review Exercises 


349  (1) 

Exponential and Logarithmic Functions 


350  (65) 


351  (11) 


362  (13) 


375  (9) 

Exponential and Logarithmic Equations 


384  (11) 

Modeling with Exponential and Logarithmic Functions 


395  (20) 


408  (1) 


409  (4) 


413  (1) 

Cumulative Review Exercises 


414  (1) 


415  (117) 


416  (14) 

Right Triangle Trigonometry 


430  (16) 

Trigonometric Functions of Any Angle 


446  (10) 

Trigonometric Functions of Real Numbers; Periodic Functions 


456  (8) 

Graphs of Sine and Cosine Functions 


464  (22) 

Graphs of Other Trigonometric Functions 


486  (12) 

Inverse Trigonometric Functions 


498  (16) 

Applications of Trigonometric Functions 


514  (18) 


525  (2) 


527  (3) 


530  (1) 

Cumulative Review Exercises 


531  (1) 


532  (54) 

Verifying Trigonometric Identities 


533  (10) 

Sum and Difference Formulas 


543  (10) 

DoubleAngle and HalfAngle Formulas 


553  (11) 

ProducttoSum and SumtoProduct Formulas 


564  (8) 


572  (14) 


582  (1) 


583  (2) 


585  (1) 

Cumulative Review Exercises 


585  (1) 

Additional Topics in Trigonometry 


586  (85) 


587  (12) 


599  (8) 


607  (11) 

Graphs of Polar Equations 


618  (12) 

Complex Numbers in Polar Form; DeMoivre's Theorem 


630  (13) 


643  (13) 


656  (15) 


665  (2) 


667  (2) 


669  (1) 

Cumulative Review Exercises 


670  (1) 

Systems of Equations and Inequalities 


671  (66) 

Systems of Linear Equations in Two Variables 


672  (14) 

Systems of Linear Equations in Three Variables 


686  (9) 


695  (9) 

Systems of Nonlinear Equations in Two Variables 


704  (9) 


713  (10) 


723  (14) 


732  (1) 


733  (3) 


736  (1) 

Cumulative Review Exercises 


736  (1) 

Matrices and Determinants 


737  (71) 

Matrix Solutions to Linear Systems 


738  (14) 

Inconsistent and Dependent Systems and Their Applications 


752  (9) 

Matrix Operations and Their Applications 


761  

Multiplicative Inverses of Matrices and Matrix Equations 


755  (35) 

Determinants and Cramer's Rule 


790  (18) 


803  (1) 


804  (2) 


806  (1) 

Cumulative Review Exercises 


807  (1) 

Conic Sections and Analytic Geometry 


808  (83) 


809  (13) 


822  (16) 


838  (12) 


850  (13) 


863  (11) 

Conic Sections in Polar Coordinates 


874  (17) 


885  (1) 


886  (2) 


888  (1) 

Cumulative Review Exercises 


889  (2) 

Sequences, Induction, and Probability 


891  (1) 

Sequences and Summation Notation 


892  (11) 


903  (9) 


911  (14) 


925  (9) 


934  (8) 

Counting Principles, Permutations, and Combinations 


942  (11) 


953  (13) 


966  (1) 


967  (2) 


969  (1) 

Cumulative Review Exercises 


970  
Appendix Where Did That Come From? Selected Proofs 

A1  

Answers to Selected Exercises 


AA1  
Subject Index 

I1  
Photo Credits 

P1  