Functions and Graphs

A very significant development in mathematics was the introduction of the Cartesian Coordinate system (or x-y coordinate system), developed by Rene Descartes (1596 - 1650). We usually draw the graph of a function using the Cartesian Coordinate system. This system made a lot of new mathematics possible, including calculus.

The graph of a function is really useful if we are trying to model a real-world problem. Sometimes we may not know an expression for a function but we do know some values (maybe from an experiment). The graph can give us a good idea of what function may be applied to the situation to solve the problem.

In this Chapter

Functions Overview

1. Introduction to Functions - definition of a function, function notation and examples

2a. Domain and Range of a Function - the x- and y-values that a function can take

2b. Functions from Verbal Statements - turning word problems into functions

Graphs of Functions

3. Rectangular Coordinates - the system we use to graph our functions

4. The Graph of a Function - examples and an application

5. Graphing Using a Computer Algebra System - some thoughts on using computers to graph functions

6. Graphs of Functions Defined by Tables of Data - often we don't have an algebraic expression for a function, just tables

7. Continuous and Discontinuous Functions - the difference becomes important in later mathematics

8. Split Functions - these have different expressions for different values of the independent variable

9. Even and Odd Functions - these are useful in more advanced mathematics

 

Let's now learn about definition of a function and function notation ».