Final answer:
To remain a function, each x-value must correspond to exactly one y-value. Adita can only add the pair (2, 1) from the options provided because it is identical to an existing pair, assuming that there are no errors in the initial set.
Step-by-step explanation:
To keep the set a function, Adita must ensure that each input in the domain (x-value) maps to exactly one output in the range (y-value). In the given set of ordered pairs, notice there is an inconsistency: the input 2 maps to more than one output (1 and 0), which violates the definition of a function.
Therefore, as the set currently stands, it is not a function. To answer the student's question, given no errors in the initial set, Adita can add an ordered pair that does not repeat an x-value already present in the set, with the exception of repeating an ordered pair that is identical to one in the set. So, the only option she could add to keep it a function, without correcting the initial mistake, would be option C) (2, 1), because it is identical to an existing ordered pair in the function. Options A), B), and D) would introduce a second output for a single input, further violating the definition of a function.