Final answer:
The student's question lacks the necessary information about the function to determine which value of c makes it one-to-one. The determination of one-to-one nature is not related to the rate of growth or magnitude provided in the reference statements.
Step-by-step explanation:
The question seems to be incomplete as the function is not provided; hence, we cannot determine the value of c for which the function is one-to-one. A one-to-one function, also known as an injective function, is a function where each input has a unique output, and no two inputs produce the same output. Without the full context of the function, it is not possible to provide the correct answer. It is also important to note that being a one-to-one function is not influenced by the factor by which a function increases; this aspect of a function is related to its rate of growth or magnitude, not its one-to-one nature.