This is the function we are trying to approximate:
This is a graph of our approximation attempt, notice they look rather similar
This is a graph of of the difference of the two functions. This graph is not on the same scale as the other two. The maximum of the other two graphs is about 2.9 while the maximum of the difference graph is about .04. So our approximation was good on the boundaries and excellent everywhere else.
All in all, this was an excellent approximation, and we were happy with the results.