Preface 

xiii  
Index of Applications 

xxv  


1  (52) 

Introduction to Real Numbers 


3  (12) 

Inequality and absolute value 


3  (3) 

Set operations and interval notation 


6  (9) 

Operations on Rational Numbers 


15  (13) 


15  (3) 

Operations on rational numbers 


18  (3) 


21  (1) 

The Order of Operations Agreement 


22  (6) 


28  (9) 

The Properties of the Real Numbers 


28  (2) 

Evaluate variable expressions 


30  (2) 

Simplify variable expressions 


32  (5) 

Verbal Expressions and Variable Expressions 


37  (16) 

Translate a verbal expression into a variable expression 


37  (2) 


39  (4) 

Focus on Problem Solving: Polya's FourStep Process 


43  (3) 

Projects and Group Activities: Water Displacement 


46  (1) 


47  (2) 


49  (1) 


50  (3) 

FirstDegree Equations and Inequalities 


53  (64) 

Equations in One Variable 


55  (10) 

Solve equations using the Addition and Multiplication Properties of Equations 


55  (3) 

Solve equations using the Distributive Property 


58  (2) 


60  (5) 

Coin, Stamp, and Integer Problems 


65  (7) 


65  (2) 


67  (5) 

Value Mixture and Motion Problems 


72  (7) 


72  (1) 


73  (6) 

Applications: Problems Involving Percent 


79  (9) 


79  (2) 


81  (7) 

Inequalities in One Variable 


88  (10) 

Solve inequalities in one variable 


88  (2) 

Solve compound inequalities 


90  (2) 


92  (6) 

Absolute Value Equations and Inequalities 


98  (19) 


98  (2) 

Absolute value inequalities 


100  (2) 


102  (4) 

Focus on Problem Solving: Understand the Problem 


106  (1) 

Projects and Group Activities: Venn Diagrams 


107  (1) 

Absolute Value Equations and Inequalities 


108  (1) 


109  (3) 


112  (1) 


113  (1) 

Cumulative Review Exercises 


114  (3) 

Linear Functions and Inequalities in Two Variables 


117  (76) 

The Rectangular Coordinate System 


119  (10) 

Points on a rectangular coordinate system 


119  (2) 

Find the length and midpoint of a line segment 


121  (2) 


123  (6) 

Introduction to Functions 


129  (13) 


129  (13) 


142  (13) 


142  (2) 

Graph an equation of the form Ax + By = C 


144  (5) 


149  (6) 


155  (9) 

Find the slope of a line given two points 


155  (3) 

Graph a line given a point and the slope 


158  (6) 

Finding Equations of Lines 


164  (8) 

Find the equation of a line given a point and the slope 


164  (2) 

Find the equation of a line given two points 


166  (1) 


167  (5) 

Parallel and Perpendicular Lines 


172  (7) 

Find equations of parallel and perpendicular lines 


172  (7) 

Inequalities in Two Variables 


179  (14) 

Graph the solution set of an inequality in two variables 


179  (3) 

Focus on Problem Solving: Find a Pattern 


182  (2) 

Projects and Group Activities: Evaluating a Function with a Graphing Calculator 


184  (1) 

Introduction to Graphing Calculators 


184  (1) 


185  (2) 


187  (3) 


190  (1) 

Cumulative Review Exercises 


191  (2) 

Systems of Equations and Inequalities 


193  (58) 

Solving Systems of Linear Equations by Graphing and by the Substitution Method 


195  (7) 

Solve a system of linear equations by graphing 


195  (2) 

Solve a system of linear equations by the substitution method 


197  (5) 

Solving Systems of Linear Equations by the Addition Method 


202  (10) 

Solve a system of two linear equations in two variables by the addition method 


202  (2) 

Solve a system of three linear equations in three variables by the addition method 


204  (8) 

Solving Systems of Equations by Using Determinants and by Using Matrices 


212  (13) 


212  (2) 

Solve systems of linear equations by using Cramer's Rule 


214  (3) 

Solve systems of linear equations by using matrices 


217  (8) 


225  (11) 

Rateofwind and watercurrent problems 


225  (2) 


227  (9) 

Solving Systems of Linear Inequalities 


236  (15) 

Graph the solution set of a system of linear inequalities 


236  (3) 

Focus on Problem Solving: Solve an Easier Problem 


239  (1) 

Projects and Group Activities: Using a Graphing Calculator to Solve a System of Equations 


240  (1) 

Solving a FirstDegree Equation with a Graphing Calculator 


241  (2) 


243  (3) 


246  (1) 


247  (2) 

Cumulative Review Exercises 


249  (2) 

Polynomials and Exponents 


251  (74) 


253  (11) 


253  (1) 

Divide monomials and simplify expressions with negative exponents 


254  (4) 


258  (1) 


259  (5) 

Introduction to Polynomials 


264  (10) 

Evaluate polynomial functions 


264  (4) 

Add or subtract polynomials 


268  (6) 

Multiplication of Polynomials 


274  (8) 

Multiply a polynomial by a monomial 


274  (1) 


275  (1) 

Multiply polynomials that have special products 


276  (1) 


277  (5) 


282  (7) 


282  (1) 


283  (2) 

Evaluate a polynomial using synthetic division 


285  (4) 


289  (11) 

Factor a monomial from a polynomial 


289  (1) 


290  (1) 

Factor trinomials of the form x2 + bx + c 


291  (2) 

Factor trinomials of the form ax2 + bx + c 


293  (7) 


300  (8) 

Factor the difference of two perfect squares and factor perfectsquare trinomials 


300  (2) 

Factor the sum or the difference of two cubes 


302  (1) 

Factor trinomials that are quadratic in form 


303  (1) 


304  (4) 

Solving Equations by Factoring 


308  (17) 

Solve equations by factoring 


308  (2) 


310  (5) 

Focus on Problem Solving: Find a Counterexample 


315  (1) 

Projects and Group Activities: Reverse Polish Notation 


316  (1) 


317  (1) 


318  (2) 


320  (2) 


322  (1) 

Cumulative Review Exercises 


323  (2) 


325  (52) 

Introduction to Rational Functions 


327  (6) 

Find the domain of a rational function 


327  (2) 

Simplify rational expressions 


329  (4) 

Operations on Rational Expressions 


333  (8) 

Multiply and divide rational expressions 


333  (1) 

Add and subtract rational expressions 


334  (7) 


341  (4) 

Simplify complex fractions 


341  (4) 


345  (10) 

Solve fractional equations 


345  (1) 


346  (2) 


348  (7) 

Proportions and Variation 


355  (10) 


355  (2) 


357  (8) 


365  (12) 


365  (2) 

Focus on Problem Solving: Implication 


367  (1) 

Projects and Group Activities: Continued Fractions 


368  (1) 

Graphing Rational Expressions 


369  (1) 


370  (2) 


372  (2) 


374  (1) 

Cumulative Review Exercises 


375  (2) 

Rational Exponents and Radicals 


377  (52) 

Rational Exponents and Radical Expressions 


379  (8) 

Simplify expressions with rational exponents 


379  (2) 

Write exponential expressions as radical expressions and radical expressions as exponential expressions 


381  (1) 

Simplify radical expressions that are roots of perfect powers 


382  (5) 

Operations on Radical Expressions 


387  (9) 

Simplify radical expressions 


387  (1) 

Add and subtract radical expressions 


388  (1) 

Multiply radical expressions 


389  (1) 

Divide radical expressions 


390  (6) 


396  (8) 


396  (2) 

Add and subtract complex numbers 


398  (1) 


398  (2) 


400  (4) 


404  (6) 

Find the domain of a radical function 


404  (1) 


405  (5) 

Solving Equations Containing Radical Expressions 


410  (19) 

Solve equations containing one or more radical expressions 


410  (2) 


412  (6) 

Focus on Problem Solving: Another Look at Polya's FourStep Process 


418  (1) 

Projects and Group Activities: Graphing Complex Numbers 


419  (2) 

Solving Radical Equations with a Graphing Calculator 


421  (1) 


422  (1) 


423  (2) 


425  (1) 

Cumulative Review Exercises 


426  (3) 

Quadratic Equations and Inequalities 


429  (66) 

Solving Quadratic Equations by Factoring or by Taking Square Roots 


431  (7) 

Solve quadratic equations by factoring 


431  (1) 

Write a quadratic equation given its solutions 


432  (1) 

Solve quadratic equations by taking square roots 


433  (5) 

Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula 


438  (11) 

Solve quadratic equations by completing the square 


438  (3) 

Solve quadratic equations by using the quadratic formula 


441  (8) 

Equations That Are Reducible to Quadratic Equations 


449  (7) 

Equations that are quadratic in form 


449  (2) 


451  (1) 


452  (4) 

Applications of Quadratic Equations 


456  (6) 


456  (6) 


462  (4) 

Solve inequalities by factoring 


462  (1) 

Solve rational inequalities 


463  (3) 

Properties of Quadratic Functions 


466  (13) 

Graph a quadratic function 


466  (4) 

Find the xintercepts of a parabola 


470  (9) 

Applications of Quadratic Functions 


479  (16) 

Minimum and maximum problems 


479  (1) 

Applications of minimum and maximum 


480  (4) 

Focus on Problem Solving: Inductive and Deductive Reasoning 


484  (1) 

Projects and Group Activities: Completing the Square 


485  (1) 

Using a Graphing Calculator to Solve a Quadratic Equation 


486  (1) 

Solving Nonlinear Inequalities Using a Graphing Calculator 


487  (1) 


488  (2) 


490  (1) 


491  (1) 

Cumulative Review Exercises 


492  (3) 


495  (44) 


497  (9) 


497  (9) 


506  (7) 

Graph by using translations 


506  (7) 


513  (5) 

Perform operations on functions 


513  (2) 

Find the composition of two functions 


515  (3) 

OnetoOne and Inverse Functions 


518  (21) 

Determine whether a function is onetoone 


518  (2) 

Find the inverse of a function 


520  (7) 

Focus on Problem Solving: Proof in Mathematics 


527  (1) 

Projects and Group Activities: Derivative Investments 


528  (2) 

Properties of Polynomials 


530  (1) 

The GreatestInteger Function 


531  (1) 


532  (2) 


534  (2) 


536  (1) 

Cumulative Review Exercises 


537  (2) 

Exponential and Logarithmic Functions 


539  (58) 


541  (9) 

Evaluate exponential functions 


541  (2) 

Graph exponential functions 


543  (7) 

Introduction to Logarithms 


550  (13) 

Write equivalent exponential and logarithmic equations 


550  (3) 

The Properties of Logarithms 


553  (10) 

Graphs of Logarithmic Functions 


563  (7) 

Graph logarithmic functions 


563  (7) 

Exponential and Logarithmic Equations 


570  (8) 

Solve exponential equations 


570  (2) 

Solve logarithmic equations 


572  (6) 

Applications of Exponential and Logarithmic Functions 


578  (19) 


578  (10) 

Focus on Problem Solving: Proof by Contradiction 


588  (1) 

Projects and Group Activities: Fractals 


589  (2) 


591  (1) 


592  (1) 


593  (1) 

Cumulative Review Exercises 


594  (3) 


597  (40) 

Introduction to Sequences and Series 


599  (6) 

Write the terms of a sequence 


599  (1) 


600  (5) 

Arithmetic Sequences and Series 


605  (7) 

Find the nth term of an arithmetic sequence 


605  (2) 

Find the sum of an arithmetic series 


607  (1) 


608  (4) 

Geometric Sequences and Series 


612  (9) 

Find the nth term of a geometric sequence 


612  (1) 


613  (2) 

Infinite geometric series 


615  (2) 


617  (4) 


621  (16) 


621  (6) 

Focus on Problem Solving: Forming Negations 


627  (1) 

Projects and Group Activities: ISBN and UPC Numbers 


628  (1) 

Finding the Proper Dosage 


629  (2) 


631  (1) 


632  (2) 


634  (1) 

Cumulative Review Exercises 


635  (2) 


637  (38) 


639  (5) 


639  (5) 


644  (6) 

Find the equation of a circle and then graph the circle 


644  (2) 

Write the equation of a circle in standard form and then graph the circle 


646  (4) 

The Ellipse and the Hyperbola 


650  (7) 

Graph an ellipse with center at the origin 


650  (2) 

Graph a hyperbola with center at the origin 


652  (5) 

Solving Nonlinear Systems of Equations 


657  (5) 

Solve nonlinear systems of equations 


657  (5) 

Quadratic Inequalities and Systems of Inequalities 


662  (13) 

Graph the solution set of a quadratic inequality in two variables 


662  (1) 

Graph the solution set of a nonlinear system of inequalities 


663  (5) 

Focus on Problem Solving: Use a Variety of ProblemSolving Strategies 


668  (1) 

Projects and Group Activities: Graphing Conic Sections Using a Graphing Utility 


668  (1) 


669  (2) 


671  (2) 


673  (2) 
Final Exam 

675  (4) 
Appendix: Guidelines for Using Graphing Calculators 

679  
Solutions to Problems 

S1  
Answers to OddNumbered Exercises 

A1  
Glossary 

G1  
Index 

I1  