As students of calculus, nothing is more important to us than functions. Other things may be more important to you in other contexts — for example, social justice, Mozart, or baseball. But this course is about functions — their various representations, their rates of growth and decay, and their uses in solving problems in many different disciplines. Thus, in this introductory chapter, we take up one big question:

What is a function?

It's very important that we have a common understanding about the answer to this question. Otherwise, it will be difficult to make much sense of the rest of the course. Furthermore, our answer to this big question may or may not agree with your previous use of the word “function” in other mathematics courses. We will start with your prior understanding and work toward a new understanding that will serve us better for your study of calculus and its uses.