To determine whether a set of ordered pairs represents a function, we must see if each input (first element of the pair) corresponds to exactly one output (second element of the pair).
A function, by definition, assigns exactly one output value to each input value. If any input value corresponds to more than one output value, the set is not a function.
Let's examine the given set of ordered pairs: [tex]\(\{(7, 3), (7, 15), (7, -11)\}\)[/tex].
1. The input [tex]\(7\)[/tex] is paired with [tex]\(3\)[/tex].
2. The input [tex]\(7\)[/tex] is also paired with [tex]\(15\)[/tex].
3. Additionally, the input [tex]\(7\)[/tex] is paired with [tex]\(-11\)[/tex].
We observe that the input value [tex]\(7\)[/tex] corresponds to multiple different output values ([tex]\(3\)[/tex], [tex]\(15\)[/tex], and [tex]\(-11\)[/tex]). This violates the definition of a function, where each input can have only one output.
Since the input value [tex]\(7\)[/tex] is associated with more than one output value, the given set of ordered pairs is not a function.
Thus, the answer to the question is:
None of the options provided forms a function.
