
Functions and Their Graphs 


1  (122) 

Investigation 1 Sales on Commission 


2  (1) 


3  (16) 

Tables, Graphs, and Equations 


3  (2) 

Choosing Scales for the Axes 


5  (2) 


7  (2) 


9  (1) 

Intercept Method for Graphing Lines 


10  (9) 


19  (20) 


19  (1) 

Functions Defined by Tables 


20  (1) 

Functions Defined by Graphs 


21  (2) 

Functions Defined by Equations 


23  (1) 


24  (1) 


25  (2) 

Operations with Function Notation 


27  (12) 


39  (17) 

Reading Function Values from a Graph 


39  (2) 

Constructing the Graph of a Function 


41  (1) 


42  (2) 

Graphical Solution of Equations and Inequalities 


44  (12) 


56  (21) 

Using Ratios for Comparison 


56  (1) 


57  (1) 


58  (1) 


59  (2) 

Lines Have Constant Slope 


61  (1) 


62  (1) 


63  (14) 


77  (15) 


77  (2) 

SlopeIntercept Method of Graphing 


79  (1) 

Finding a Linear Equation from a Graph 


80  (1) 


81  (11) 


92  (31) 

Fitting a Line through Two Points 


92  (1) 


93  (2) 


95  (2) 

Linear Interpolation and Extrapolation 


97  (14) 


111  (9) 


120  (3) 


123  (110) 

Investigation 2 Epidemics 


124  (1) 

Investigations 3 Perimeter and Area 


125  (1) 


126  (13) 

Solving Nonlinear Equations 


126  (2) 


128  (1) 


128  (1) 

Compound Interest and Inflation 


129  (1) 

Other Nonlinear Equations 


130  (9) 


139  (15) 


139  (2) 


141  (1) 

Investigation 4 Eight Basic Functions 


142  (2) 

Graphs of Eight Basic Functions 


144  (1) 

Properties of the Basic Functions 


144  (2) 

Functions Defined Piecewise 


146  (8) 

Transformations of Graphs 


154  (21) 


154  (2) 


156  (3) 


159  (16) 

Functions as Mathematical Models 


175  (17) 


175  (3) 

Using the Basic Functions as Models 


178  (2) 

Modeling with Piecewise Functions 


180  (12) 

The Absolute Value Function 


192  (11) 


193  (2) 

Absolute Value Inequalities 


195  (1) 

Using the Absolute Value in Modeling 


196  (2) 


198  (5) 


203  (30) 

Definitions of Domain and Range 


203  (1) 

Finding Domain and Range from a Graph 


204  (3) 

Finding the Domain from a Formula 


207  (1) 


208  (7) 


215  (9) 


224  (9) 


233  (88) 

Investigation 5 Inflating a Balloon 


234  (1) 


235  (20) 


235  (2) 

The Scaling Property of Direct Variation 


237  (2) 

Finding a Formula for Direct Variation 


239  (1) 

Direct Variation with a Power of x 


240  (1) 


241  (1) 


242  (2) 

Finding a Formula for Inverse Variation 


244  (11) 


255  (13) 


255  (2) 


257  (3) 

Working with Negative Exponents 


260  (1) 


260  (8) 


268  (14) 


268  (1) 

Exponential Notation for Radicals 


268  (2) 


270  (1) 

Using Fractional Exponents to Solve Equations 


271  (1) 


272  (1) 

Solving Radical Equations 


273  (2) 

A Note on Roots of Negative Numbers 


275  (7) 


282  (15) 


282  (1) 


283  (1) 


284  (1) 


285  (1) 

Operations with Rational Exponents 


286  (1) 


287  (1) 

Investigation 6 Vampire Bats 


287  (10) 


297  (24) 

Functions of Two or More Variables 


297  (1) 


298  (1) 


299  (3) 


302  (9) 


311  (7) 


318  (3) 


321  (80) 

Investigation 7 Population Growth 


322  (1) 

Exponential Growth and Decay 


323  (17) 


323  (1) 


324  (1) 


325  (3) 


328  (1) 

Investigation 8 Exponential Decay 


328  (1) 


329  (2) 

Comparing Linear Growth and Exponential Growth 


331  (9) 


340  (15) 

Graphs of Exponential Functions 


340  (2) 

Transformations of Exponential Functions 


342  (1) 

Comparing Exponential and Power Functions 


343  (1) 


344  (2) 

Graphical Solution of Exponential Equations 


346  (9) 


355  (10) 

Using the Conversion Equations 


357  (1) 


357  (2) 


359  (1) 

Solving Exponential Equations 


359  (2) 

Application to Exponential Models 


361  (4) 


365  (11) 

Using the Properties of Logarithms 


366  (1) 

Solving Exponential Equations 


367  (2) 


369  (1) 


370  (1) 


371  (5) 


376  (25) 

Fitting an Exponential Function through Two Points 


376  (2) 


378  (3) 


381  (1) 

Annuities and Amortization 


382  (9) 


391  (6) 


397  (4) 


401  (74) 


402  (19) 

Finding a Formula for the Inverse Function 


403  (1) 

Inverse Function Notation 


404  (2) 

Graph of the Inverse Function 


406  (1) 

When Is the Inverse a Function? 


407  (2) 

Mathematical Properties of the Inverse Function 


409  (1) 


410  (2) 


412  (9) 


421  (16) 

Inverse of the Exponential Function 


421  (3) 

Graphs of Logarithmic Functions 


424  (2) 

Evaluating Logarithmic Functions 


426  (1) 


426  (2) 

Using the Properties of Logarithms 


428  (7) 

Investigation 9 Interest Compounded Continuously 


435  (2) 


437  (14) 

The Natural Exponential Function 


437  (1) 

The Natural Logarithmic Function 


438  (1) 

Properties of the Natural Logarithm 


439  (1) 


440  (1) 

Exponential Growth and Decay 


441  (2) 


443  (8) 


451  (24) 


453  (1) 

Equal Increments on a Log Scale 


454  (2) 


456  (2) 


458  (1) 


459  (7) 


466  (6) 


472  (3) 


475  (86) 

Investigation 10 Height of a Baseball 


476  (1) 


477  (12) 


477  (1) 

Solving Quadratic Equations by Factoring 


478  (3) 


481  (1) 

Solutions of Quadratic Equations 


481  (1) 

Equations Quadratic in Form 


482  (7) 

Solving Quadratic Equations 


489  (12) 


489  (2) 

Solving Quadratic Equations by Completing the Square 


491  (2) 


493  (2) 


495  (1) 


496  (5) 


501  (14) 


501  (1) 


502  (1) 

The Graph of y = ax2 + bx 


503  (1) 


504  (1) 

The Graph of y = ax2 + bx + c 


505  (1) 


506  (1) 


507  (8) 


515  (13) 

Investigation 11 Revenue from Theater Tickets 


515  (1) 

Maximum or Minimum Values 


516  (1) 

The Vertex Form for a Parabola 


517  (2) 

Graphing with the Vertex Form 


519  (1) 

Systems Involving Quadratic Equations 


519  (9) 


528  (10) 

Solving Inequalities Graphically 


528  (3) 

Solving Quadratic Inequalities Algebraically 


531  (7) 


538  (23) 

Finding a Quadratic Function through Three Points 


539  (3) 

Finding an Equation in Vertex Form 


542  (10) 


552  (6) 


558  (3) 

Polynomial and Rational Functions 


561  (76) 

Investigations 12 Bezier Curves 


562  (3) 


565  (12) 


566  (1) 


567  (1) 


568  (1) 

Modeling with Polynomials 


569  (8) 

Graphing Polynomial Functions 


577  (11) 

Classifying Polynomials by Degree 


577  (1) 


578  (1) 


579  (1) 

xIntercepts and the Factor Theorem 


580  (2) 

Zeros of Multiplicity Two or Three 


582  (6) 


588  (12) 


588  (1) 


589  (1) 

Arithmetic of Complex Numbers 


590  (1) 

Products of Complex Numbers 


591  (1) 

Quotients of Complex Numbers 


592  (1) 


593  (2) 


595  (5) 

Graphing Rational Functions 


600  (17) 

Domain of a Rational Function 


603  (1) 


604  (2) 


606  (2) 


608  (9) 

Equations That Include Algebraic Fractions 


617  (20) 

Solving Equations with Fractions Algebraically 


618  (1) 

Solving Equations with Fractions Graphically 


619  (1) 


619  (2) 


621  (6) 


627  (6) 


633  (4) 


637  (70) 

Investigation 13 Interpolating Polynomials 


638  (1) 

Systems of Linear Equations in Two Variables 


639  (15) 

Solving Systems by Graphing 


639  (4) 

Inconsistent and Dependent Systems 


643  (3) 


646  (2) 

An Application from Economics 


648  (6) 

Systems of Linear Equations in Three Variables 


654  (12) 


654  (2) 


656  (1) 


657  (3) 

Inconsistent and Dependent Systems 


660  (1) 


661  (5) 

Solving Linear Systems Using Matrices 


666  (16) 

Coefficient Matrix and Augmented Matrix of a System 


667  (1) 

Elementary Row Operations 


667  (3) 


670  (1) 


671  (2) 


673  (7) 

Investigation 14 InputOutput Models 


680  (2) 


682  (8) 

Graphs of Inequalities in Two Variables 


682  (1) 


683  (1) 


684  (2) 


686  (4) 


690  (17) 

The Objective Function and Constraints 


690  (1) 


691  (1) 


692  (8) 


700  (5) 


705  (2) 

APPENDIX A Algebra Skills Refresher 


707  (90) 


707  (6) 


707  (1) 

Parentheses and Fraction Bars 


707  (1) 


708  (1) 


709  (4) 

Linear Equations and Inequalities 


713  (7) 


713  (2) 


715  (1) 


716  (1) 


717  (3) 

Algebraic Expressions and Problem Solving 


720  (9) 


722  (1) 


722  (1) 


723  (1) 


724  (5) 


729  (7) 


729  (1) 


730  (6) 

Linear Systems in Two Variables 


736  (7) 

Solving Systems by Substitution 


736  (1) 

Solving Systems by Elimination 


737  (6) 


743  (6) 


743  (1) 


744  (1) 


745  (1) 


746  (1) 


746  (3) 

Polynomials and Factoring 


749  (7) 


749  (1) 


750  (1) 


751  (1) 


751  (1) 


751  (1) 


752  (1) 


752  (4) 

Factoring Quadratic Trinomials 


756  (5) 

Special Products and Factors 


758  (3) 

Working with Algebraic Fractions 


761  (12) 


761  (2) 


763  (1) 


764  (1) 

Sums and Differences of Like Fractions 


764  (1) 

Lowest Common Denominator 


765  (1) 


766  (1) 

Sums and Differences of Unlike Fractions 


766  (2) 


768  (1) 


769  (4) 


773  (9) 


773  (1) 


773  (2) 

Sums and Differences of Radicals 


775  (1) 


775  (1) 

Rationalizing the Denominator 


776  (1) 


777  (1) 

Extraneous Solutions to Radical Equations 


778  (1) 

Equations with More than One Radical 


779  (3) 


782  (10) 

Right Triangles and the Pythagorean Theorem 


782  (1) 

Isosceles and Equilateral Triangles 


783  (1) 


783  (1) 


784  (1) 


785  (1) 


786  (1) 


787  (1) 


788  (4) 


792  (5) 

Subsets of the Real Numbers 


792  (1) 


793  (1) 


793  (1) 

Properties of the Real Numbers 


794  (1) 

Order Properties of the Real Numbers 


795  (2) 

APPENDIX B Using a Graphing Calculator 


797  (12) 


797  (1) 


797  (1) 


797  (1) 


798  (1) 


798  (3) 


798  (1) 


799  (1) 


799  (1) 


800  (1) 


801  (1) 


801  (1) 


801  (1) 


801  (1) 


802  (1) 


802  (1) 


802  (3) 


802  (1) 


803  (1) 


803  (1) 


803  (1) 


804  (1) 


804  (1) 


805  (1) 


805  (1) 


805  (1) 


806  (1) 


806  (1) 

Finding a Regression Equation 


806  (1) 

Graphing the Regression Equation 


807  (1) 

Function Notation and Transformations of Graphs 


807  (2) 


807  (1) 


808  (1) 
Glossary 

809  (10) 
Bibliography 

819  
Answers to OddNumbered Problems 

1  (1) 
Index 

1  