This first chapter establishes the foundation for the rest of the text. We will begin by introducing the more general concept of a relation, and show how a relation may be viewed algebraically, numerically, and graphically. We will then see how a function is a very special type of relation and learn to use functional notation and terminology. We will next discuss various algebraic manipulations with functions, beginning with the most fundament operations of composition and inversion, and concluding with various miscellaneous operations.
The text will be interspersed with short sets of Exercises, indicated by a 
icon. These Exercises are an important part of the learning process, not
simply hurdles to be jumped (or crawled under). Although complete
solutions to most Exercises are included, make sure to make an honest effort to
solve them before
looking at the solutions. In other math courses, you may have developed
the habit of "working backwards" from an answer in the back of a
textbook. This habit short-circuits the learning process and robs
you of their full benefit.
Unlike other textbooks, you should notice that the solutions are written in complete English sentences. Likewise, there are not a lot of repetitive, mechanical Exercises. If you have developed the habit of working as quickly as possible through a series of similar, drill problems to "get them out of the way", you will need to develop new habits. That is because, this text provides only a few brief Exercises linked to the main concepts in the text. The intent is to encourage you to think very carefully about a few, well-chosen problems so that you can learn as much as possible while doing them.
Although it is more time-consuming, you should use the solutions as a model, and try to write out your solutions as completely as possible. While you may not realize it yet, the process of fully verbalizing your own thoughts is very helpful in cementing your understanding of concepts and uncovering the gaps and misconceptions in your thinking. The Exercise sets are deliberately made to be short, so that you will have plenty of time to think carefully about each Exercise.
It is crucial that you pay close attention to the material in the following sections, even if you think you already know it all, and especially if it all seems new. Since these sections establish the foundation for the rest of the text, the more effort you put in now, the easier a time you will have the subsequent chapters.
Go to Relations
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