Chapter 3

Relations and functions

Chapter description
We now build on the work of the previous two chapters to introduce functions. These are very important in scientific and engineering applications, and this chapter helps you to understand how they work.
It is split up into the following sections.

1. Two special kinds of relationship
   1. Direct proportion
   2. Some physical examples of direct proportion
   3. More exotic examples
   4. Partial direct proportion -- lines not through the origin
   5. Inverse proportion
   6. Some examples of mixed variation

2. An introduction to functions
   1. What are functions? Some relationships examined
   2. y = f(x) -- a useful new shorthand
   3. When is a relationship a function?
   4. Stretching and shifting -- new functions from old
   5. Two practical examples of stretching and shifting
   6. Finding functions of functions
   7. Can we go back the other way? Inverse functions
   8. Finding inverses of more complicated functions
   9. Sketching the particular case of f(x) = (x+3)/(x-2) and its inverse
   10. Odd and even functions

3. Exponential and log functions
   1. Exponential functions -- describing population growth
   2. The inverse of a growth function: log functions
   3. Finding the logs of some particular numbers
   4. The three laws or rules for logs
   5. What are `e' and `exp'? A brief introduction
   6. Negative exponential functions -- describing population decay

4. Unveiling secrets -- logs and linear forms
   1. Example (1) Relationships of the form y=axⁿ
   2. Example (2) Relationships of the form y=an^x
   3. What can we do if logs are no help?

---

You can click here to look at the contents of Chapter 4
or you can click here to return to my home page.

---