Final answer:
Only one of the statements provided by the student is correct: f(-6) = 10. This is because it matches the ordered pair (-6, 10) from the set representing the function f(x).
Step-by-step explanation:
From the student's question regarding the function f(x) represented by a set of ordered pairs, none of the proposed statements -f(-3) = 8, f(3) = 5, f(8) = 0- are correct, because the pairs provided do not contain these specific inputs (x-values).
The correct statement is f(-6) = 10, as it directly matches one of the ordered pairs in the set.
To explain, a function f(x) is defined by its ordered pairs, where each x-value has exactly one y-value assigned to it.
Looking at the set provided {(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)}, the first element of each pair is the x-value and the second is its corresponding y-value.
Therefore, the only correct option from those listed by the student is f(-6) = 10 which is backed up by the ordered pair (-6, 10).
Understanding functions and their representations through ordered pairs is crucial for analyzing mathematical relationships and for graphing such functions accurately.