4. Functions

In our daily life, we deal with charts, graphs, tables of numbers, formulas, etc. In fact, these are devices for qualitative description of certain relations between two groups of objects. Specific types of these relations are called functions.

Functions are of great importance in the entire modern mathematics. Particularly, in calculus, we talk about functions all the time. We find the limit of functions, we differentiate functions, and we integrate functions.

In this chapter, some of the topics that we talk about are:

• The definition of functions, their domain, codomain, and range
• Graphs of functions
• How to distinguish a function from other types of relations by looking at its graph
• Odd and even functions
• Elementary functions that we see most of the time in calculus
• Constructing new functions from the old ones
• Increasing and decreasing functions
• Inverse functions
• Periodic functions

Functions that cannot be expressed in terms of a finite sequence of algebraic operations are studied in a separate chapter.