Final answer:
To make a relation no longer a function, eliminate the ordered pair (-4,1) because doing so violates the vertical line test required for a relation to be a function. Therefore, the correct answer is A.
Step-by-step explanation:
To determine which ordered pair should be eliminated to ensure that a given relation is no longer a function, we need to understand what it means for a relation to be a function. A relation is a function if and only if each input (or x-value) is associated with exactly one output (or y-value). If we apply the vertical line test, which states that a vertical line drawn through the graph of a relation should not intersect the graph at more than one point, we can determine whether it is a function.
In the ordered pairs (-4,1) and (1,-4), the x-values are -4 and 1, respectively. If we were to eliminate the pair (1,-4), the x-value 1 would no longer have a corresponding y-value, thus maintaining the function's criteria. However, if we eliminate the pair (-4,1), the x-value -4 would still have a corresponding y-value, which means that the relation would still pass the vertical line test and therefore remain a function. So option B is incorrect because the horizontal line test is irrelevant to the definition of a function, and options C and D are incorrect as well because the relation would still be a function regardless of which pair is removed. Thus, the correct answer is:
A) Eliminate (-4,1); it results in a relation that is not a function because it violates the vertical line test.