This pair / small group activity gives students an opportunity to apply what they know about limits, with the option of including continuity as well. Each group gets a card with various requirements* and must sketch a graph on poster paper that has the given characteristics.
There are twelve cards: six that have characteristics about the continuity of the function, and six that do not. So you have the option of using this activity before or after students have learned about continuity.
*Example requirements on each card:
f(-1) is undefined
the limit as x approaches 4 from the left is -3
the limit as x approaches 2 is not equal to f(2)
there is a jump discontinuity at x = 4