
Algebra Background for Precalculus 


1  (34) 


1  (5) 


6  (5) 

Polynomials and Factoring 


11  (9) 


20  (15) 

Coordinates, Graphs, and Inequalities 


35  (66) 


35  (12) 

Graphs and Equations, A Second Look 


47  (10) 


57  (12) 


69  (8) 


77  (8) 


85  (16) 


101  (74) 

The Definition of a Function 


101  (12) 


113  (17) 


130  (12) 

Methods of Combining Functions. Iteration 


142  (12) 


154  (21) 

Polynomial and Rational Functions. Applications to Iteration and Optimization 


175  (95) 


175  (14) 


189  (9) 

More on Iteration. Quadratics and Population Growth 


198  (17) 

Applied Functions: Setting up Equations 


215  (12) 

Maximum and Minimum Problems 


227  (11) 


238  (13) 


251  (19) 

Exponential and Logarithmic Functions 


270  (87) 


271  (9) 

The Exponential Function y = ex 


280  (9) 


289  (12) 


301  (9) 

Equations and Inequalities with Logs and Exponents 


310  (11) 


321  (11) 

Exponential Growth and Decay 


332  (25) 

Trigonometric Functions of Angles 


357  (51) 

Trigonometric Functions of Acute Angles 


357  (10) 

Algebra and the Trigonometric Functions 


367  (7) 

RightTriangle Applications 


374  (9) 

Trigonometric Functions of Angles 


383  (12) 


395  (13) 

Trigonometric Functions of Real Numbers 


408  (75) 


408  (9) 

Radian Measure and Geometry 


417  (10) 

Trigonometric Functions of Real Numbers 


427  (11) 

Graphs of the Sine and the Cosine Functions 


438  (16) 

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


454  (8) 


462  (5) 

Graphs of the Tangent and the Reciprocal Functions 


467  (16) 


483  (55) 


483  (9) 

The DoubleAngle Formulas 


492  (10) 

The ProducttoSum and SumtoProduct Formulas 


502  (5) 


507  (11) 

The Inverse Trigonometric Functions 


518  (20) 

Additional Topics in Trigonometry 


538  (62) 

The Law of Sines and the Law of Cosines 


538  (15) 

Vectors in the Plane, A Geometric Approach 


553  (7) 

Vectors in the Plane, An Algebraic Approach 


560  (8) 


568  (8) 

Introduction to Polar Coordinates 


576  (9) 

Curves in Polar Coordinates 


585  (15) 


600  (72) 

Systems of Two Linear Equations in Two Unknowns 


600  (11) 


611  (8) 


619  (12) 

The Inverse of a Square Matrix 


631  (7) 

Determinants and Cramer's Rule 


638  (13) 

Nonlinear Systems of Equations 


651  (7) 


658  (14) 


672  (80) 


672  (9) 


681  (11) 

Tangents to Parabolas (Optional) 


692  (3) 


695  (15) 


710  (11) 

The FocusDirectrix Property of Conics 


721  (9) 

The Conics in Polar Coordinates 


730  (6) 


736  (16) 

Roots of Polynomial Equations 


752  (70) 

The Complex Number System 


752  (8) 


760  (7) 

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


767  (8) 

The Fundamental Theorem of Algebra 


775  (9) 

Rational and Irrational Roots 


784  (8) 

Conjugate Roots and Descartes's Rule of Signs 


792  (6) 

Introduction to Partial Fractions 


798  (7) 

More About Partial Fractions 


805  (17) 


822  (33) 


822  (6) 


828  (10) 

Introduction to Sequences and Series 


838  (7) 

Arithmetic Sequences and Series 


845  (5) 

Geometric Sequences and Series 


850  (5) 


855  
APPENDIXES 

A1  

A.1 Using a Graphing Utility 


A3  

A.2 Significant Digits and Calculators 


A7  

A.3 Properties of the Real Numbers 


A11  


A18  

A.5 Review of Integer Exponents and n th Roots 


A19  

A.6 Review of Rational Exponents 


A26  
TABLES 

A29  


A30  

2 Logarithms to the Base Ten 


A31  


A33  

4 Values of Trigonometric Functions 


A34  
Answers to Selected Exercises 

A41  
Index 

I1  