Education Technology

Exploring Families of Functions

Published on 08/10/2005

Activity Overview

This activity provides students an opportunity to discover the similarities involved in shifting the parent functions for absolute value, quadratic, cubic, radical, exponential, and logarithmic functions. Students will also be given the opportunity to write the equation of a given graph.

Before the Activity

If you are using the TI-Navigator System with the TI-73 you will need the attached .pdf file.

  • Students should be familiar with entering equations into the graphing calculator, as well as obtaining the table of values for that graph.

  • Students should also be familiar with sending a list, an equation, and a graph to the teacher via TI-Navigator™

  • Define the term parent function and discuss how y = x represents the parent function for linear equations.

  • Using linear functions as a model, discuss what the terms shift, dilation, and reflection mean.
  • During the Activity

  • Divide students into groups of 6. Assign each group one of the families of functions listed above.

  • As a group, they are to determine the parent function for that family of functions. They will be sending the graph of the parent function and the table of values to the teacher via TI-Navigator&trade.

  • After finding the parent function, students should then be directed to add and subtract values from the end of the parent function. Students will then consult the graph and table of values to make a conclusion about how the parent function is affected by a value being added/subtracted at the end of the parent function.

  • Students then should be directed to place parentheses around the x variable only. Inside parentheses, students should add and subtract values from x. After consulting the graph and table of values, students will draw conclusions regarding how the parent function is affected by adding/subtracting a value from the x coordinate.

  • Students then should be directed to place a positive value in front of the x coordinate (or in front of the parentheses). After consulting the graph and the table of values, students will draw conclusions.

  • Students then will do the same procedure as #5, but will investigate how a negative value in front of the x coordinate (or in front of the parentheses) affects the graph.

  • Students will practice shifting, reflecting, and dilating graphs of their particular function based on the conclusions drawn above.

  • After allowing the groups to draw conclusions regarding the shifting, reflecting, and dilating of their particular family of functions, each group will get 5-7 minutes to present their conclusions to the class.
  • After the Activity

  • Each member of the group should draft an equation from the family of functions they discussed in their group. He/she should enter this equation in y1 and graph the equation.

  • Using the screen capture feature of TI-Navigator™, the teacher should choose one graph at random.

  • Students should then work to write an equation for the graph shown on the screen.

  • The Learning Check file attached can be used to test students on the material covered in class. Send the LearningCheck™ file out via TI-Navigator™.