Step 1 :The given relation is \(\{(7,8),(9,9),(-5,-5),(-4,4)\}\).
Step 2 :The domain of a relation is the set of all first elements (x-values) in the ordered pairs, and the range is the set of all second elements (y-values).
Step 3 :The domain of the relation is \(\{7,9,-5,-4\}\).
Step 4 :The range of the relation is \(\{8,9,-5,4\}\).
Step 5 :To find the maximum and minimum of the x-values and y-values, we need to find the highest and lowest values in the domain and range, respectively.
Step 6 :The maximum x-value is \(9\), the minimum x-value is \(-5\).
Step 7 :The maximum y-value is \(9\), the minimum y-value is \(-5\).
Step 8 :Final Answer: The maximum x-value is \(\boxed{9}\), the minimum x-value is \(\boxed{-5}\), the maximum y-value is \(\boxed{9}\), and the minimum y-value is \(\boxed{-5}\).