I worked through this community center task for interpreting graphs at a 2013 Common Core Workshop I attended (OGAP). I am blogging about the activities we did last summer so that they are easier for me to find when I go to plan lessons. I hope these ideas will inspire you as well.
I believe this task is from CPM. They claim that the task is adapted from The Language of Functions and Graphs, Joint Matriculation Board, Shell Centre for Mathematical
Education, 1985. I found a PDF shared online. This task is on page 15.
During the workshop, we classified this activity as addressing the following Common Core Standards: F-IF.4, F-IF.5, F-IF.6. We also added several other questions to this activity.
I did this problem with my Algebra 2 students this year, and they struggled with it majorly! I gave it as a homework assignment that most did not turn in. The students who came to me for one-on-one help were able to grasp the activity, but few came to me for help.