Chapter 0 Variables, functions and graphs
If we count pre-calculus/trigonometry as a pre-requisite, then functions and their graphs are a pre-pre-requisite! But that doesn’t mean that you have familiarity with every aspect of these. Recognition of basic types of functions is crucial for being able to use mathematics for modeling and to handle material at the pace and level you will need. So is the ability to go back and forth between analytic expressions for functions and their graphs. So is number sense: knowing approximate values without stopping for a detailed calculation. So is knowledge of how to use physical units in a math problem. We expect most of these to be unfamiliar to many of you, and have included explanations and some homework; this may be challenging, even though it is on pre-college material. We hope it will be at least somewhat interesting!
In addition, there are some more routine things to discuss up front. In order to have a shared language, we need to agree on notation and terminology. Normally it is a good idea to read everything that is assigned; however if this notation is very familiar, you can probably just answer the self-check questions and skip the reading. We apologize for the length of this preliminary section. When the material becomes harder, the sections will be shorter.
