Pre-Calculus All-in-One For Dummies

Chapter 4

Operating on Functions

IN THIS CHAPTER

Transforming one function into many others

Performing different operations on functions

Finding and verifying inverses of functions

A basic mathematical function serves as the model or parent for many, many other functions. By just adding or subtracting numbers, or multiplying or dividing by numbers, a parent function can be slid around, flipped, stretched, and squashed. The basic function is usually still recognizable and most of its properties are in place. It makes life easier not to have to add completely different functions to the mix; you just have to do some minor adjustments to the original.

The basic operations on rational numbers also apply to functions. But there’s a whole new operation that applies only to combining functions — composition. It’s somewhat like composing a musical number; you insert certain patterns of sounds in different parts of the arrangement to make something totally wonderful.

Inverse functions undo the operations of the original function. Just like inverse operations undo something another operation has done, inverse functions operate to undo other functions.

Transforming the Parent Graphs

In certain ...