
1 ALGEBRA BACKGROUND FOR PRECALCULUS 


1  (34) 


1  (5) 


6  (5) 

1.3 Polynomials and Factoring 


11  (9) 


20  (15) 

2 COORDINATES, GRAPHS, AND INEQUALITIES 


35  (66) 

2.1 Rectangular Coordinates 


35  (12) 

2.2 Graphs and Equations, a Second Look 


47  (10) 


57  (12) 


69  (8) 


77  (8) 


85  (16) 


101  (74) 

3.1 The Definition of a Function 


101  (12) 

3.2 The Graph of a Function 


113  (17) 

3.3 Techniques in Graphing 


130  (12) 

3.4 Methods of Combining Functions. Iteration 


142  (12) 


154  (21) 

4 POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO ITERATION AND OPTIMIZATION 


175  (95) 


175  (14) 


189  (9) 

4.3 More on Iteration. Quadratics and Population Growth 


198  (17) 

4.4 Applied Functions: Setting Up Equations 


215  (12) 

4.5 Maximum and Minimum Problems 


227  (11) 


238  (13) 


251  (19) 

5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 


270  (87) 

5.1 Exponential Functions 


271  (9) 

5.2 The Exponential Function y = e(x) 


280  (9) 

5.3 Logarithmic Functions 


289  (12) 

5.4 Properties of Logarithms 


301  (9) 

5.5 Equations and Inequalities with Logs and Exponents 


310  (11) 


321  (11) 

5.7 Exponential Growth and Decay 


332  (25) 

6 THE TRIGONOMETRIC FUNCTIONS 


357  (59) 


357  (14) 

6.2 Trigonometric Functions of Angles 


371  (11) 

6.3 Evaluating the Trigonometric Functions 


382  (8) 

6.4 Algebra and the Trigonometric Functions 


390  (10) 

6.5 RightTriangle Trigonometry 


400  (16) 

7 GRAPHS OF THE TRIGONOMETRIC FUNCTIONS 


416  (62) 

7.1 Trigonometric Functions of Real Numbers 


417  (11) 

7.2 Graphs of the Sine and Cosine Functions 


428  (16) 

7.3 Graphs of y = A sin(Bx  C) and y = A cos(Bx  C) 


444  (12) 

7.4 Simple Harmonic Motion 


456  (6) 

7.5 Graphs of the Tangent and the Reciprocal Functions 


462  (16) 

8 ANALYTICAL TRIGONOMETRY 


478  (59) 

8.1 The Addition Formulas 


478  (9) 

8.2 The DoubleAngle Formulas 


487  (10) 

8.3 ProducttoSum and SumtoProduct Formulas 


497  (5) 

8.4 Trigonometric Equations 


502  (14) 

8.5 The Inverse Trigonometric Functions 


516  (21) 

9 ADDITIONAL TOPICS IN TRIGONOMETRY 


537  (79) 

9.1 RightTriangle Applications 


537  (14) 

9.2 The Law of Sines and the Law of Cosines 


551  (16) 

9.3 Vectors in the Plane, a Geometric Approach 


567  (7) 

9.4 Vectors in the Plane, an Algebraic Approach 


574  (8) 


582  (12) 

9.6 Introduction to Polar Coordinates 


594  (5) 

9.7 Graphs in Polar Coordinates 


599  (17) 


616  (72) 

10.1 Systems of Two Linear Equations in Two Unknowns 


616  (11) 

10.2 Gaussian Elimination 


627  (8) 


635  (12) 

10.4 The Inverse of a Square Matrix 


647  (7) 

10.5 Determinants and Cramer's Rule 


654  (13) 

10.6 Nonlinear Systems of Equations 


667  (7) 

10.7 Systems of Inequalities 


674  (14) 


688  (80) 


688  (9) 


697  (11) 

11.3 Tangents to Parabolas (Optional) 


708  (3) 


711  (15) 


726  (11) 

11.6 The FocusDirectrix Property of Conics 


737  (9) 

11.7 The Conics in Polar Coordinates 


746  (6) 


752  (16) 

12 ROOTS OF POLYNOMIAL EQUATIONS 


768  (70) 

12.1 The Complex Number System 


768  (8) 

12.2 Division of Polynomials 


776  (7) 

12.3 Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem 


783  (8) 

12.4 The Fundamental Theorem of Algebra 


791  (9) 

12.5 Rational and Irrational Roots 


800  (8) 

12.6 Conjugate Roots and Descartes's Rule of Signs 


808  (6) 

12.7 Introduction to Partial Fractions 


814  (7) 

12.8 More About Partial Fractions 


821  (17) 


838  

13.1 Mathematical Induction 


838  (6) 

13.2 The Binomial Theorem 


844  (10) 

13.3 Introduction to Sequences and Series 


854  (7) 

13.4 Arithmetic Sequences and Series 


861  (5) 

13.5 Geometric Sequences and Series 


866  (5) 


871  


A1  (28) 

A.1 Using a Graphing Utility 


A3  (4) 

A.2 Significant Digits and Calculators 


A7  (4) 

A.3 Properties of the Real Numbers 


A11  (7) 


A18  (1) 

A.5 Review of Integer Exponents and nth Roots 


A19  (7) 

A.6 Review of Rational Exponents 


A26  (3) 


A29  (12) 


A30  (1) 

2 Logarithms to the Base Ten 


A31  (2) 


A33  (1) 

4 Values of Trigonometric Functions 


A34  (7) 
ANSWERS TO SELECTED EXERCISES 

A41  
INDEX 

I1  