The most appropriate viewing window for determining the domain and range of the function f(x) = (x^2 - 81)/(x^2 - 11x + 18) would be:
Xmin: -10, Xmax: 10
Ymin: -10, Ymax: 10
This window allows you to see a wide range of x-values and y-values, giving you a comprehensive view of the graph and helping you determine the domain and range of the function accurately.