Final answer:
The value of c that would prevent the relation from being a function is 3, as it would result in the same input having two different outputs in the relation.
Step-by-step explanation:
The student is asking which value of c cannot be substituted into the relation {(3,5), (6,–7),(c, 2),(0,5)} in order for it to remain a function. A function, by definition, has only one output value for each input value. Therefore, we must look for a value of c that is already used as an input with a different output value within the relation. In the given relation, the input values are 3, 6, and 0. The only value from the options provided that is already used as an input is 3. Hence, if we substitute c with 3, we will have two different output values (2 and 5) for the same input, which disqualifies the relation from being a function.
The correct answer is B. 3, because substituting c with 3 would result in the pair (3,2), which, combined with the existing pair (3,5), would mean the relation has two different output values for the same input value of 3.