Final answer:
The given set B does not represent a function because the x-value '5' is associated with two different y-values. However, the domain of B is {2, 4, 5, 8} and the range is {1, 3, 4, 5, -9}.
Step-by-step explanation:
The given set B = {(2,1),(4,3), (5,4), (5,5), (8,-9)} represents the points of a relation. To determine if this set represents a function, we need to check if each input, or x-value, is associated with exactly one output, or y-value. In a function, every element in the domain (the set of all possible x-values) must be associated with only one element in the range (the set of all possible y-values).
In this case, we see that the x-value '5' is associated with two different y-values '4' and '5'. Therefore, the given set B does not define a function because it violates the definition of a function by having a single input corresponding to multiple outputs.
The domain of a relation is the set of all x-values. For the given set B, the domain is {2, 4, 5, 8}. The range consists of all the y-values, which for B are {1, 3, 4, 5, -9}.