This virtual manipulative is designed to teach the concept of a function by allowing you to experiment with various functions. This animation helps students to understand the function concept through the "machine" metaphor. The domain elements (input) are dragged into the machine, which then goes through some (unseen) process and spits out the range element corresponding to the input. The results are then displayed in tabular form.
Drag each number into the function machine and look for a pattern that will allow you to complete the table.
You can experiement with functions right on the Internet or download a free trial desktop version.