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Precalculus

Introduction to Polynomial and Rational Functions

PrecalculusIntroduction to Polynomial and Rational Functions
35-mm film and SD cards
35-mm film, once the standard for capturing photographic images, has been made largely obsolete by digital photography. (credit “film”: modification of work by Horia Varlan; credit “memory cards”: modification of work by Paul Hudson)

Chapter Outline

3.1 Complex Numbers
3.2 Quadratic Functions
3.3 Power Functions and Polynomial Functions
3.4 Graphs of Polynomial Functions
3.5 Dividing Polynomials
3.6 Zeros of Polynomial Functions
3.7 Rational Functions
3.8 Inverses and Radical Functions
3.9 Modeling Using Variation

Digital photography has dramatically changed the nature of photography. No longer is an image etched in the emulsion on a roll of film. Instead, nearly every aspect of recording and manipulating images is now governed by mathematics. An image becomes a series of numbers, representing the characteristics of light striking an image sensor. When we open an image file, software on a camera or computer interprets the numbers and converts them to a visual image. Photo editing software uses complex polynomials to transform images, allowing us to manipulate the image in order to crop details, change the color palette, and add special effects. Inverse functions make it possible to convert from one file format to another. In this chapter, we will learn about these concepts and discover how mathematics can be used in such applications.

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