Preface 

xiii  


xvii  
To the Student 

xix  

Functions, Graphs, and Models; Linear Functions 


1  (138) 


2  (8) 


2  (1) 


3  (1) 

Inequalities and Intervals on the Number Line 


4  (1) 


5  (1) 


5  (1) 


6  (1) 


6  (2) 


8  (1) 


8  (2) 


10  (17) 


10  (2) 


12  (2) 


14  (2) 


16  (1) 


17  (10) 


27  (14) 


27  (1) 


28  (4) 


32  (1) 

Determining Viewing Windows 


32  (2) 


34  (7) 


41  (14) 


41  (1) 


42  (3) 


45  (2) 

Slope and yIntercept of a Line 


47  (2) 


49  (1) 

Parallel and Perpendicular Lines 


50  (5) 


55  (15) 

Writing Equations of Lines 


55  (5) 


60  (2) 

Approximately Linear Data 


62  (8) 

Algebraic and Graphical Solutions of Linear Equations 


70  (12) 

Algebraic Solution of Linear Equations 


71  (2) 

Solutions, Zeros, and xlntercepts 


73  (1) 

Graphical Solution of Linear Equations 


74  (3) 

Formulas; Solving an Equation for a Specified Linear Variable 


77  (5) 

Fitting Lines to Data Points; Modeling Linear Functions 


82  (20) 

Fitting Lines to Data Points 


82  (3) 


85  (3) 

Modeling Discrete Data with Linear Functions 


88  (4) 


92  (1) 


92  (10) 

Systems of Linear Equations in Two Variables 


102  (12) 

Graphical Solution of Systems 


102  (3) 


105  (2) 


107  (1) 

Modeling Systems of Linear Equations 


108  (2) 

Inconsistent and Dependent Systems 


110  (4) 

Solutions of Linear Inequalities 


114  (25) 

Algebraic Solution of Linear Inequalities 


114  (3) 

Graphical Solution of Linear Inequalities 


117  (2) 


119  (1) 


120  (6) 


126  (1) 

Key Concepts and Formulas 


126  (5) 


131  (1) 


132  (5) 

Group Activities/Extended Applications 


137  (2) 

Quadratic and Other Nonlinear Functions 


139  (136) 


140  (14) 


140  (1) 


141  (1) 

Radicals and Rational Exponents 


142  (1) 


143  (1) 

Multiplication of Polynomials 


144  (2) 


146  (3) 

Solving Literal Equations 


149  (1) 

Imaginary and Complex Numbers 


149  (1) 

Operations with Complex Numbers 


150  (4) 

Quadratic Functions; Parabolas 


154  (11) 


154  (5) 

Quadratic Functions in the Form f(x) = a(x  h)2 + k 


159  (1) 


160  (5) 

Solving Quadratic Equations 


165  (16) 


165  (2) 


167  (1) 

Combining Graphs and Factoring 


168  (2) 

Graphical and Numerical Methods 


170  (1) 


170  (1) 


171  (1) 


172  (2) 


174  (1) 

Aids for Solving Quadratic Equations 


175  (1) 

Equations with Compiex Solutions 


175  (6) 


181  (12) 


181  (4) 


185  (2) 

PiecewiseDefined Functions 


187  (2) 


189  (4) 

Transformations of Graphs and Symmetry 


193  (15) 

Shifts of Graphs of Functions 


193  (3) 

Stretching and Compressing Graphs 


196  (1) 


197  (3) 

Symmetry; Even and Odd Functions 


200  (8) 

Quadratic and Power Models 


208  (17) 

Modeling with Quadratic Functions 


208  (1) 

Comparison of Linear and Quadratic Models 


209  (3) 

Modeling with Power Functions 


212  (2) 

Comparison of Power and Quadratic Models 


214  (11) 

Combining Functions; Composite Functions 


225  (12) 

Operations with Functions 


225  (1) 

Revenue, Cost, and Profit 


226  (3) 


229  (8) 


237  (12) 


237  (6) 

Inverse Functions on Limited Domains 


243  (6) 

Additional Equations and Inequalities 


249  (26) 

Radical Equations; Equations Involving Rational Powers 


249  (2) 

Equations Containing Rational Powers 


251  (1) 

Solving Absolute Value Equations 


252  (1) 

Inequalities Involving Absolute Values 


253  (1) 

Solution of Quadratic Inequalities 


254  (4) 


258  (3) 


261  (1) 

Key Concepts and Formulas 


262  (4) 


266  (1) 


267  (6) 

Group Activities/Extended Applications 


273  (2) 

Exponential and Logarithmic Functions 


275  (94) 


276  (5) 

Zero and Negative Exponents 


276  (2) 


278  (1) 


279  (2) 


281  (10) 


281  (1) 

Transformations of Graphs of Exponential Functions 


282  (1) 


283  (2) 


285  (1) 


286  (5) 


291  (12) 


291  (4) 


295  (2) 


297  (2) 

Solution of Logarithmic Equations 


299  (4) 

Exponential and Logarithmic Equations; Properties of Logarithms 


303  (14) 

Solving Exponential Equations Using Logarithmic Forms 


303  (2) 


305  (3) 


308  (2) 

Solving Exponential Equations Using Logarithmic Properties 


310  (2) 

Solution of Logarithmic Equations 


312  (1) 


313  (4) 

Exponential and Logarithmic Models 


317  (15) 

Modeling with Exponential Functions 


317  (3) 

Constant Percent Change in Exponential Models 


320  (2) 


322  (1) 


323  (1) 


324  (3) 

Exponents, Logarithms, and Linear Regression 


327  (5) 

Exponential Functions and Investing 


332  (9) 


332  (2) 

Continuous Compounding and the Number e 


334  (3) 

Present Value of an Investment 


337  (1) 


338  (3) 

Annuities; Loan Repayment 


341  (8) 

Future Value of an Annuity 


341  (2) 

Present Value of an Annuity 


343  (1) 


344  (5) 

Logistic and Gompertz Functions 


349  (20) 


349  (5) 


354  (5) 


359  (1) 

Key Concepts and Formulas 


359  (3) 


362  (1) 


363  (4) 

Group Activities/Extended Applications 


367  (2) 

HigherDegree Polynomial and Rational Functions 


369  (76) 


370  (7) 


370  (1) 

Factoring HigherDegree Polynomials 


370  (1) 


371  (1) 

Multiplying and Dividing Rational Expressions 


372  (1) 

Adding and Subtracting Rational Expressions 


373  (1) 


374  (3) 

HigherDegree Polynomial Functions 


377  (10) 


378  (3) 


381  (6) 

Modeling Cubic and Quartic Functions 


387  (13) 

Modeling with Cubic Functions 


387  (3) 

Modeling with Quartic Functions 


390  (1) 


391  (1) 

Third and Fourth Differences 


392  (8) 

Solution of Polynomial Equations 


400  (10) 

Solving Polynomial Equations by Factoring 


400  (3) 

Solution Using Factoring by Grouping 


403  (1) 


403  (2) 

Estimating Solutions with Technology 


405  (5) 

Polynomial Equations Continued; Fundamental Theorem of Algebra 


410  (10) 

Division of Polynomials; Synthetic Division 


410  (2) 

Using Synthetic Division to Solve Cubic Equations 


412  (1) 


412  (2) 


414  (2) 

Fundamental Theorem of Algebra 


416  (4) 

Rational Functions and Rational Equations 


420  (11) 

Graphs of Rational Functions 


420  (5) 

Analytical and Graphical Solution of Rational Equations 


425  (6) 

Polynomial and Rational Inequalities 


431  (14) 


431  (2) 


433  (4) 


437  (1) 

Key Concepts and Formutas 


437  (3) 


440  (1) 


441  (2) 

Group Activities/Extended Applications 


443  (2) 

Systems of Equations and Matrices 


445  (74) 


446  (4) 


446  (1) 


447  (1) 

Linear Equations in Three Variables 


447  (3) 

Systems of Linear Equations in Three Variables 


450  (11) 

Systems in Three Variables 


450  (1) 

LefttoRight Elimination 


451  (2) 

Modeling Systems of Equations 


453  (1) 


454  (7) 

Matrix Solution of Systems of Linear Equations 


461  (14) 

Matrix Representation of Systems of Equations 


461  (1) 

Echelon Forms of Matrices; Solving Systems with Matrices 


462  (2) 


464  (1) 


465  (1) 


466  (1) 


467  (2) 


469  (6) 


475  (15) 

Addition and Subtraction of Matrices 


475  (4) 

Multiplication of a Matrix by a Number 


479  (1) 


480  (3) 

Multiplication with Technology 


483  (7) 

Inverse Matrices; Matrix Equations 


490  (14) 


490  (2) 


492  (1) 

Encoding and Decoding Messages 


493  (3) 


496  (2) 

Matrix Equations and Technology 


498  (6) 

Systems of Nonlinear Equations 


504  (15) 

Algebraic Solution of Nonlinear Systems 


504  (3) 

Graphical Solution of Nonlinear Systems 


507  (4) 


511  (1) 

Key Concepts and Formulas 


511  (2) 


513  (1) 


514  (3) 

Group Activities/Extended Applications 


517  (2) 

Special Topics: Systems of Inequalities and Linear Programming; Sequences and Series; Preparing for Calculus 


519  


520  (12) 

Linear Inequalities in Two Variables 


520  (2) 

Systems of Inequalities in Two Variables 


522  (4) 

Systems of Nonlinear inequalities 


526  (6) 

Linear Programming: Graphical Methods 


532  (11) 


532  (6) 


538  (5) 

Sequences and Discrete Functions 


543  (9) 


543  (2) 


545  (2) 


547  (5) 


552  (8) 

Finite and Infinite Series 


552  (1) 


553  (2) 


555  (2) 

Infinite Geometric Series 


557  (3) 


560  


560  (2) 


562  (3) 


565  (1) 


566  (4) 


570  (1) 

Key Concepts and Formulas 


570  (2) 


572  (1) 


573  (2) 

Group Activity/Extended Application 


575  
Answers to Selected Exercises 

1  (1) 
Index 

1  