Functional representations like

V(t) = a + bt

do not describe a unique function, but rather a closely related collection of functions. All of the functions in the collection have similar behaviors – just like a family. Indeed, we call these collections families of functions.

Think of a family's shared functional form as the DNA that links the family members together. Think of each choice of parameter as an expression of a particular gene (e.g., brown eyes or blue eyes). Just as it's possible to recognize the parents and siblings of someone you know, you'll learn to recognize certain families of functions by becoming acquainted with some typical members.

Although there are infinitely many functions to choose from when trying to model natural phenomena, data often falls into a few common patterns. To describe the world, one doesn't need to be familiar with every function on the planet. It is sufficient, in many circumstances, to be well-acquainted with just a handful of hard-working families.

In the examples that follow, we will dig through the closets of some of these families, look at the different representations that they wear, and learn the secrets behind their behaviors.