


Numbers and Their Disguises 



Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals 


1  (24) 





Completing the square in one and two variables 


25  (5) 





Equations of degree 1 and 2, solving other types of equations, rational equations, the zerofactor property 


30  (17) 

Algebraic Functions and Graphs 



Functions and Their Graphs 



Introduction, equations of lines, power functions, shifting graphs, intersection of curves 


47  (28) 



Cyclic Phenomena: The Six Basic Trigonometric Functions 



Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas 


75  (20) 



The family of exponential functions, the function ex 


95  (6) 

Composition and Inverse Functions 



Composite functions, the idea of inverses, finding an inverse of f given by a graph, finding the inverse of f given by an expression 


101  (12) 



Definition of logarithms, logarithms as inverses of exponential functions, laws of logarithms, the natural logarithm 


113  (13) 

Inverse Trigonometric Functions 



The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric identities 


126  (13) 



Changing the Form of a Function 



Factoring, canceling, long division, rationalizing, extracting a factor from under a root 


139  (14) 



Simplifying Algebraic Expressions 



Working with difference quotients and rational functions, canceling common factors, rationalizing expressions 


153  (7) 



Decomposition of Functions 



Inner, outer, and outermost functions, decomposing composite functions 


160  (2) 



Equations of Degree 1 Revisited 



Solving linear equations involving derivatives 


162  (4) 

Related Rates, Applied MaxMin Problems 



Word Problems, Algebraic and Transcendental 



Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay 


166  (12) 

Integrating Trigonometric Functions 





Rewriting trigonometric expressions using identities 


178  (5) 

Appendices (Use as needed) 




183  (3) 

Derivation of the Quadratic Formula 


186  (3) 
Answers to OddNumbered Exercises 

189  (22) 
Index 

211  