Final answer:
To determine the missing ordered pair, each x-value from the given list must only be paired with one unique y-value, as per the definition of a function. All presented options, except D, have either conflicting x or y values with the existing ordered pairs. Option D (-3,-4) is the missing pair as it has a unique x-value not present in the list.
Step-by-step explanation:
The question involves determining which ordered pair is missing from a given list, making sure that the list represents a function. A function has a unique output value for each input value, which means each x-value in the list of ordered pairs must be paired with only one y-value.
Here's how to identify the missing ordered pair from the provided options: Examine the list of given ordered pairs, and check for any x-values that are duplicated. If any x-value appears more than once, the corresponding y-values must be different; if not, it would imply that one x-value is related to multiple y-values, which would violate the definition of a function.
Looking at the given ordered pairs:
(12,6),(3,1),(2,-2),(5,10),(-8,-4)
We observe that all the x-values are unique, meaning no x-value is paired with more than one y-value. Therefore, none of the provided options A. (2,1), B. (12,7), C. (-8,8), or D. (-3,-4) indicate pairs that would complete the function. In fact, option D (-3,-4) does not conflict with the existing pairs, as -3 is not an x-value that appears in the given list of ordered pairs.