Park City Mathematics Institute
Visualizing Functions
Project Abstracts

Drafts of Project Files (password required)

A User's Guide to Function Notation
Matthew Carpenter*, Douglas Lutz

Use this lesson to help students learn and understand function notation. The goal of this activity is for students to make a connection between the input and output relation of functions and how that relates to function notation. Using the Fathom computer software, students will create data for six different functions. Using non-traditional functions that alter words into numbers and visa versa, and traditional functions that take numbers to numbers, students will discover how to express functions using function notation. They will also be asked a series of questions that relate to function notation as well as properties of functions.

Function Cards
Gregory Monson, Mario Shaunette*

Function Cards display different aspects of a function. Each could be a text description, an equation, a data table, or a graph. Any kind of function can be included from linear to exponential to compound to inverses. They can be used

  • when teaching the characteristics of a function type
  • to reinforce the notion of what a function is
  • to review the differences between function types
  • to practice recognition of characteristics that identify function types.
Sinusoid Curve Fitting with Fathom
Matthew Bracher*

The purpose of this activity is for students to explore the effects of the amplitude, period, phase shift, and midline on the graph of a sinusoid by manipulating those parameters until their graph matches the one Fathom generates.

Functional Life
Craig Morgan, Rebecca Neighborgall*, Monte Saxby

These lessons are designed to introduce students to the basics of functions without using numeric values. The first lesson begins with concrete rules of subtracting and adding coins followed by a second lesson introducing functions and notation by looking at slicing ingredients for and making pizza. The final lesson has students manipulating functions that transform the letters in words.

* denotes contact author

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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.