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. Its maximum is about .0009, while the other two have the maximum of about 1.7. Overall, this is an excellent approximation, especially away from the boundaries.
All in all, this was an excellent approximation, and we were happy with the results.