The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function `c=30.75u+5.75,`where `u` is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the domain of the function for this situation?

Since the number of players on the volleyball team must be at least 8 and at most 12, the domain of the function is the set of integers between 8 and 12 (inclusive). Therefore, the domain is $\boxed{\{8,9,10,11,12\}}$.