Forging Connections
Identify Function Families
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The members of a function family resemble each other. You will explore the behavior of functions to determine which ones belong to the same family.

1 Family Resemblances

On each page of this sketch you’ll analyze four functions to determine which one belongs to a different family from the other three. As part of your investigation you'll compare the relative motion of the two variables (both direction and speed), compare the shapes and sizes of the traces they make, and check each function for fixed points.

Worksheet

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2 Objectives

This page supports the Identify Families lesson from Unit 1: Introducing Geometric Transformations as Functions.

By the end of this lesson, you’ll be able to perform these actions and answer these questions:

  • Drag input variables and observe and describe the behavior of output variables.
  • Distinguish between functions based on the shapes traced by the variables.
  • Distinguish between functions based on relative speed and direction of variables.
  • Distinguish between functions based on the presence and nature of fixed points.
  • Describe several function families based on the similarity of their features.
  • Formulate a working definition of a function family.
  • Determine whether a function belongs to a particular family.

3 The Fine Print

Requirements:

These activities require web access using a browser that supports HTML5 and JavaScript. (That means almost any current browser.) No purchase is required, and there’s no advertising anywhere.

Release Information

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Update History:

03 Apr 2018: Revised the worksheet and objectives.
21 Oct 2017: Migrated from GF to FC format
18 Oct 2015: Updated this page to the website format.