Place magnets on the backs of the graphs. Also, laminating the graphs will help to protect them for future use.
Put a series of the graphs on the board for the class to see. Hold in your hand a matching number of graphs that will be potential inverse graphs of the ones on the board. Ask for volunteers (or choose students) to take a graph from you and put it with its inverse on the board. If you want a more challenging activity, place graphs in the pile that do not have their inverses on the board (you might want to warn the class of this possibility so as not to be "too" mean!!!).
This exercise can be done with inverse relations (such as the examples below) or inverse functions.
Prepare several of the graphs "close" in style so that there is some