Park City Mathematics Institute
Visualizing Functions
Project Abstract

Drafts of Project Files (password required)

Function Transformations of Iggy the Iguana
Clint Chan, Donald Helvie, Teri Hulbert*
This mini-unit (week long series of lessons) is meant to help students understand the transformation rules for general functions and not just memorize them. They will begin with non-algebraic general functions and then move towards being able to link the algebraic representation with the visual representation of other functions (and some relations). The use of both Powerpoint and student tasks will reinforce the visual aspects of transformations. An application of image transformation will conclude the experience to offer a realistic situation involving the concepts.
Solving Polynomial & Rational Inequalities
Joseph Ochiltree*, Katya Orfanova-Malikov
Developed from a pattern noticed by a participant when solving polynomial inequalities, the first two worksheets lead the student to notice the link between end behavior, the leading term of the polynomial and the effect on solutions to inequalities. Further explorations using GeoGebra develop the role of patterning in polynomials in factored form.
Christopher Luzniak*, Jamie Smith
PixelMath is a soon-to-be released open-source tool developed by Dr. Steve Tanimoto at the University of Washington as part of the METIP (Mathematics Experiences through Image Processing) project. The Java applet is designed to work with image transformations based on functions rather than clickable Photoshop-like tools. The article discusses real life examples of functions that are used to move a lot of points in an image in different ways and develops the ideas of domain and range when students pushing into working with images rather than the number line. Step-by-step instructions on how to do function transformation with PixelMath are included so that students can actively experiment with image transformations.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.