Research+Question+8

=Research Question 8= // (Zac, Sara, Mike, Leah) //

How is the behavior of this sequence connected to what we learned about groups?

Are there more than 2 types of groups (finite and infinite)? -Raschelle

 Ryan- Use the group that you already know to be finite and see how it is connected to iteration instead of finding new groups. For instance, how the functions would give the identity after 2-4 iterations.

1. Is there a rubric that predicts what groups will be finite or infinite? -Paul 2. Does it apply to just functions that are groups? -Cassie 3. Are there any patterns in the number of iterations between groups? -Jordan

1. Are there specific types of functions (i.e., 1/x) that, when iterated, form a group? Do they have to be divergent, alternating functions? - Myles 2. Does composing different functions with each other result in certain groups? - Katy

If you take the functions from one of the groups we had in the last lab and compose them with each other, will they be a finite/infinite group? -Megan