In This Chapter
Figuring out functions and relations
Learning about lines
Getting particular about parabolas
Grappling with graphs
Transforming functions and investigating inverse functions
Virtually everything you do in calculus concerns functions and their graphs in one way or another. Differential calculus involves finding the slope or steepness of various functions, and integral calculus involves computing the area underneath functions. And not only is the concept of a function critical for calculus, it’s one of the most fundamental ideas in all of mathematics.
Basically, a function is a relationship between two things in which the numerical value of one thing in some way depends on the value of the other. Examples are all around us: The average daily temperature for your city depends on, and is a function of, the time of year; the distance an object has fallen is a function of how much time has elapsed since ...