# Example 1

A software program can show a user how far he or she is from a location on a map. Zadie is walking in a straight line down her street. For any time , in seconds, her distance from her home, in feet, can be represented by the function . Create a graph to show Zadie’s distance from her house. Which point on the graph shows when Zadie has reached her house?
1. Determine a domain for the problem statement.
2. Determine the range for the given domain.
3. Find the critical point of the absolute value function.
4. Determine whether the critical point is a minimum or a maximum.
5. Find at least two additional points on the graph. One should have an input less than the critical point, and the other should have an input greater than the critical point.
6. Use the three points to create the graph of the function on the determined domain.
7. Interpret the graph to find when Zadie will arrive at her house.
This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit www.walch.com for more information on their resources.