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:
- Constants, Variables, and Parameters
- Concept of a Function
- Natural Domain and Range of a Function
- Graphs of Functions
- Vertical Line Test
- Domain and Range Using Graph
- Piecewise-Defined Functions
- Equal Functions
- Even and Odd Functions
- Examples of Elementary Functions
- Transformations of Functions
- Algebraic Combination of Functions
- Composition of Functions
- Increasing or Decreasing Functions
- One-to-One 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.