ABSTRACT
The fourth chapter introduces the concept of a function and presents many proofs for functions in general. It defines odd and even functions and shows that any function with a symmetric domain is a sum of an odd and an even function. Then it defines composite, monotonic, and inverse functions and establishes their properties. For example, one section shows a great way to invert a composite function by splitting a tough problem into several easy ones. Then the chapter defines the rules for applying a function to both sides of an inequality, which is often a source of difficulty for students. The chapter concludes with a treatment of convex and concave functions. These types of functions are important in many applications and have a number of interesting properties.
