In the functions module we continue our focus on the structure and meaning of algebraic expressions, but apply them to the concept of function. Functions are to algebra what variables are to arithmetic. Just as in algebra, variables are used to represent numbers, in the study of functions we use letters to represent entire functional relationships. Our goal in this section is to sort out the relationship between these levels of abstraction, and develop ways of thinking about functions that would help high school students see the difference between them.
Extended analysis of a high school mathematics problem (see sidebar).
Definition of logarithm, deriving the properties of logarithms from the properties of exponents.
Comparison of growth rates of power functions and exponential functions. Development of a proof that exponentials grow faster than powers.