This is an investigative task designed to allow students to discover the shape of the graph of absolute value functions and to apply their knowledge of the behavior of functions to a new function type. Students create tables and sketch the graphs of several absolute value functions, predicting the changes that would occur in each case. Students then draw conclusions about the relationship between the general form of an absolute value function and its graph and use these conclusions to write absolute value functions that meet certain conditions and to compare the graphs of various absolute value functions.
This task was designed for use in an Honors Advanced Algebra (Algebra 2) class, but could be easily used in an on-level Algebra 2 course.
This file contains the fully editable task, as well as a completed answer key.