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, the topics that we talk about are:

  1. Constants, Variables, and Parameters
  2. Concept of a Function
  3. Natural Domain and Range of a Function
  4. Graphs of Functions
  5. Vertical Line Test
  6. Domain and Range Using Graph
  7. Piecewise-Defined Functions
  8. Equal Functions
  9. Even and Odd Functions
  10. Examples of Elementary Functions
  11. Transformations of Functions
  12. Algebraic Combination of Functions
  13. Composition of Functions
  14. Increasing or Decreasing Functions
  15. One-to-One Functions
  16. Inverse Functions
  17. Periodic Functions

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