A yo-yo is oscillating vertically between heights of $1$$1$ and $3$ feet above the floor. 

1. Sketch a graph of this situation.

   Hint (a):

   When you sketch your graph, scale the $y$-axis but not the $x$-axis.

2. Suppose the yo-yo is now going up and down twice as fast. Sketch a graph of this new situation on top of your graph from part (a). How do these graphs compare?

   Hint (b):

   The "period" is twice as fast, the vertical heights remain the same.

3. Finally, suppose the yo-yo is going up and down one third as fast as its original rate. Sketch a graph of this situation on top of your graph from part (a). How does it compare to the original graph?

   Hint (c):

   The "period" is now three times slower.