This activity should be given after the students have seen linear, absolute value, quadratic, polynomial, and radical graphs. It has the students match each functions graph, equation, table of values, and verbal description. Students who finish early can work on creating their own cube root graphs as an extension.
This is a great activity that takes around 45 minutes. I think that it is best to group students homogeneously, but heterogeneous grouping is fine as well. I would laminate the cut outs so that they can be easily used each year.