Preserving the function requires adding a point not present in the original set. Option A) (-5,7) fulfills this condition, ensuring the function's integrity.
The relationship between sets A and B is crucially defined by whether each element in A corresponds to at least one element in B. Functions, a specific type of relation, further impose the condition that each element in A (the domain) has a unique mapping to an element in B (the range).
Examining the given options, the original set of values for A and B is as follows:
X Y
6 -9
-8 9
-1 -4
9 -6
8 -8
To preserve the function, the additional point selected must not disrupt the unique mapping of each element in A to an element in B. Among the choices, x=9, x=-8, and x=-1 already have defined values in Y, and introducing a new value for any of them would violate the function condition.
The only viable choice to preserve the function is option A) (-5,7), as -5 is not present in the original set of X values. By adding this point, the function remains intact, adhering to the one-to-one mapping between A and B.