To preserve the function, the new point must adhere to the rule that each x-value corresponds to only one y-value. Among the choices, only (−5, 7) satisfies this rule.
A function is a relationship between two sets, where each element in the first set (the domain) is associated with exactly one element in the second set (the range). In other words, for every input (x-value), there is only one output (y-value).
Looking at the table, we can see that for each x-value, there is only one y-value. For example, when x is 6, y is 6. When x is -1, y is -4. And so on.
Therefore, to preserve the function, any new point that is added to the table must follow this rule. Of the four choices, only (−5, 7) satisfies this rule. For x = -5, y = 7.
* Choice B) (9, −5) would violate the function because there is already a point in the table where x = 9 (y = 6).
* Choice C) (−1, −5) would violate the function because there is already a point in the table where x = -1 (y = -4).
* Choice D) (−8, −6) would violate the function because the y-value (-6) is not associated with the x-value (-8) in any other point in the table.
Therefore, the only choice that preserves the function is A) (−5, 7).