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.
The cartesian plane
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
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.