Final answer:
The value for a that makes the relation R a function is D. 0, because this value is not already used as an input, thus avoiding the repetition that would disqualify it from being a function.
Step-by-step explanation:
The student has asked which replacement for a in the relation R = {(−2,4), (a,7), (3,10), (6,13)} makes it a function. A relation is a function if each input (x-coordinate) is associated with exactly one output (y-coordinate). In the given relation, there are already inputs with values -2, 3, and 6. To avoid repeated inputs, which would disqualify it from being a function, a cannot be 3 or 6 as they are already present.
Therefore, the correct replacement for a that makes this relation a function is D. 0. Option D, or 0, is not already an input and would therefore maintain the criteria for the relation to be a function.