Final answer:
A function requires that each input is paired with exactly one output. The relations B and C are functions because they consist of pairs with unique first elements, whereas A and D do not meet the criteria for being functions.
Step-by-step explanation:
The function is a special kind of relation where each input is related to exactly one output. To determine which relation is also a function from the given options, we need to find a set of pairs where no two different pairs have the same first element.
- A. {(4, 8), (8, 4), (4, 12), (20, 16), (12, 16)} - Not a function because the input '4' has two different outputs '8' and '12'.
- B. {(8, 4), (4, 8), (12, 4), (16, 20), (20, 12)} - This is a function because all the first elements are unique.
- C. {(10, 15), (15, 20)} - This is also a function since both pairs have unique first elements.
- D. {(x^2, 10), (20, 25)} - Not a function because 'x^2' is not a specific value, and if x took on multiple values that resulted in the same x^2, this would violate the function rule.
Thus, the relations that are also functions are options B and C.