Here we will look at elementary functions, these serve as basic building blocks for other function; we will also look at functions that are quite useful or at least interesting. Covering elementary functions is usually done "by parts". You start with them at the beginning, because without them it is hard to do anything in math. On the other hand, since you start with them early, you did not really cover anything yet, so it is equally hard to say anything about them. This presents a big problem for lecturers and authors of books, since they must somehow follow a line of exposition that makes sense. Since here we have all info available by clicking, we can afford to simply collect all important information about elementary functions to one place; if you look at some and encounter a notion you are not familiar with, you can always check on it in some part of Math Tutor.
By the way, a one-page summary of the important facts concerning trig and hyperbolic functions is here as a pdf file. A similar one-page overview of other elementary functions can be found here.
Elementary functions:
Useful functions: These are used in various applications.
Interesting functions: This is a freak zoo, these functions usually serve as a warning and a safety check. If you think that something might be true for all functions, you should start by checking whether it works for these beauties.