
Part I Solutions to OddNumbered Exercises 


1  (624) 

Functions and Their Graphs 



Section 1.1 Rectangular Coordinates 


2  (5) 

Section 1.2 Graphs of Equations 


7  (5) 

Section 1.3 Linear Equations in Two Variables 


12  (7) 


19  (6) 

Section 1.5 Analyzing Graphs of Functions 


25  (6) 

Section 1.6 A Library of Parent Functions 


31  (4) 

Section 1.7 Transformations of Functions 


35  (8) 

Section 1.8 Combinations of Functions: Composite Functions 


43  (5) 

Section 1.9 Inverse Functions 


48  (8) 

Section 1.10 Mathematical Modeling and Variation 


56  (20) 


60  (10) 


70  (3) 


73  (3) 

Polynomial and Rational Functions 



Section 2.1 Quadratic Functions and Models 


76  (8) 

Section 2.2 Polynomial Functions of Higher Degree 


84  (9) 

Section 2.3 Polynomial and Synthetic Division 


93  (7) 

Section 2.4 Complex Numbers 


100  (4) 

Section 2.5 Zeros of Polynomial Functions 


104  (10) 

Section 2.6 Rational Functions 


114  (9) 

Section 2.7 Nonlinear Inequalities 


123  (25) 


132  (11) 


143  (2) 


145  (3) 

Exponential and Logarithmic Functions 



Section 3.1 Exponential Functions and Their Graphs 


148  (4) 

Section 3.2 Logarithmic Functions and Their Graphs 


152  (5) 

Section 3.3 Properties of Logarithms 


157  (4) 

Section 3.4 Exponential and Logarithmic Equations 


161  (7) 

Section 3.5 Exponential and Logarithmic Models 


168  (18) 


175  (7) 


182  (2) 


184  (2) 



Section 4.1 Radian and Degree Measure 


186  (5) 

Section 4.2 Trigonometric Functions: The Unit Circle 


191  (3) 

Section 4.3 Right Triangle Trigonometry 


194  (6) 

Section 4.4 Trigonometric Functions of Any Angle 


200  (6) 

Section 4.5 Graphs of Sine and Cosine Functions 


206  (7) 

Section 4.6 Graphs of Other Trigonometric Functions 


213  (6) 

Section 4.7 Inverse Trigonometric Functions 


219  (6) 

Section 4.8 Applications and Models 


225  (16) 


230  (7) 


237  (2) 


239  (2) 



Section 5.1 Using Fundamental Identities 


241  (7) 

Section 5.2 Verifying Trigonometric Identities 


248  (4) 

Section 5.3 Solving Trigonometric Equations 


252  (6) 

Section 5.4 Sum and Difference Formulas 


258  (9) 

Section 5.5 MultipleAngle and ProducttoSum Formulas 


267  (24) 


279  (7) 


286  (3) 


289  (2) 

Additional Topics in Trigonometry 




291  (4) 

Section 6.2 Law of Cosines 


295  (5) 

Section 6.3 Vectors in the Plane 


300  (6) 

Section 6.4 Vectors and Dot Products 


306  (5) 

Section 6.5 Trigonometric Form of a Complex Number 


311  (21) 


321  (7) 


328  (2) 


330  (2) 

Systems of Equations and Inequalities 



Section 7.1 Linear and Nonlinear Systems of Equations 


332  (7) 

Section 7.2 TwoVariable Linear Systems 


339  (7) 

Section 7.3 Multivariable Linear Systems 


346  (12) 

Section 7.4 Partial Fractions 


358  (7) 

Section 7.5 Systems of Inequalities 


365  (6) 

Section 7.6 Linear Programming 


371  (21) 


377  (8) 


385  (4) 


389  (3) 

Matrices and Determinants 



Section 8.1 Matrices and Systems of Equations 


392  (8) 

Section 8.2 Operations with Matrices 


400  (7) 

Section 8.3 The Inverse of a Square Matrix 


407  (8) 

Section 8.4 The Determinant of a Square Matrix 


415  (6) 

Section 8.5 Applications of Matrices and Determinants 


421  (23) 


427  (11) 


438  (3) 


441  (3) 

Sequences, Series, and Probability 



Section 9.1 Sequences and Series 


444  (6) 

Section 9.2 Arithmetic Sequences and Partial Sums 


450  (4) 

Section 9.3 Geometric Sequences and Series 


454  (7) 

Section 9.4 Mathematical Induction 


461  (8) 

Section 9.5 The Binomial Theorem 


469  (5) 

Section 9.6 Counting Principles 


474  (3) 


477  (13) 


480  (5) 


485  (3) 


488  (2) 

Topics in Analytic Geometry 




490  (4) 

Section 10.2 Introduction to Conics: Parabolas 


494  (5) 


499  (6) 


505  (6) 

Section 10.5 Rotation of Conics 


511  (9) 

Section 10.6 Parametric Equations 


520  (7) 

Section 10.7 Polar Coordinates 


527  (5) 

Section 10.8 Graphs of Polar Equations 


532  (6) 

Section 10.9 Polar Equations of Conics 


538  (19) 


544  (8) 


552  (3) 


555  (2) 

APPENDIX A Review of Fundamental Concepts of Algebra 



Appendix A.1 Review of Real Numbers and Their Properties 


557  (5) 

Appendix A.2 Exponents and Radicals 


562  (4) 

Appendix A.3 Polynomials and Factoring 


566  (7) 

Appendix A.4 Rational Expressions 


573  (4) 

Appendix A.5 Solving Equations 


577  (12) 

Appendix A.6 Linear Inequalities in One Variable 


589  (5) 

Appendix A.7 Errors and the Algebra of Calculus 


594  (4) 

Solutions to Practice Tests 


598  (27) 

Part II Solutions to Chapter and Cumulative Tests 


625  