Functions and Graphs

By M Bourne

In the real world, it's very common that one quantity depends on another quantity.

For example, if you work in a fast food outlet, your pay packet depends on the number of hours you work. Or, the amount of concrete you need to order when constructing a building will depend on the height of the building.

This chapter is about functions (this is how we express relationships between quantities) and their graphs.

The graph of a function is really useful if we are trying to model a real-world problem. ("Modeling" is the process of finding the relationships between quantities.)

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

2. 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

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

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.