1. The problem asks to find the domain and range of the function given by the set of points $\{(1,5), (3,-2), (5,1), (7,-5)\}$. 2. The domain of a function is the set of all possible input values (x-values). 3. The range of a function is the set of all possible output values (y-values). 4. From the given points, the domain is the set of all x-values: $\{1, 3, 5, 7\}$. 5. The range is the set of all y-values: $\{5, -2, 1, -5\}$. 6. Therefore, the domain is $\{1, 3, 5, 7\}$ and the range is $\{5, -2, 1, -5\}$.