Final answer:
Without specific mappings of domain and range elements, we cannot definitively determine if the given relations are functions. The examples provided do not contain sufficient information to make a conclusive judgment about the relations being functions.
Step-by-step explanation:
To determine whether a relation is a function, we must check if each element in the domain corresponds to exactly one element in the range. That is, no domain element should be associated with more than one range element. With this in mind, let's evaluate the options:
- a) Domain: {-4, 3.9, 7, 5}; Range: {-9, -3, -2, -6, 113}; Not a function. Without more information, we cannot determine if it's not a function based solely on the domain and range sets.
- b) Domain: {3.9, -4, 7, 5}; Range: {-9, -3, -2, -6, 113}; Function. The statement claims it's a function, and unless a domain element is paired with more than one range element, we must assume it's true.
- c) Domain: {-9, -3, -2, -6, 113}; Range: {-4, 3.9, 7, 5}; Not a function. Same as in option 'a', we cannot declare it's not a function without additional details.
- d) Domain: {-9, -3, -2, -6, 113}; Range: {3.9, -4, 7, 5}; Function. As before, if each domain value is paired with only one range value, this statement is valid.
Without specific pairings of the domain and range elements, we cannot definitively state whether the relation is a function. It could be or could not be a function depending on the specific mapping of pairs. However, the options given do not provide enough detail to make this determination.