Final answer:
The student mistakenly thinks that a function cannot have the same value in the range for two different inputs, but a function only requires that each input has a unique output.
Step-by-step explanation:
The student's error lies in misunderstanding the definition of a function in mathematics. A function is a relation in which each element of the domain (which are the x-values, or inputs) is paired with exactly one element of the range (the y-values, or outputs). The relation provided, {(2,1), (3,-2), (4,5), (5,-2)}, does indeed qualify as a function because no single domain value is paired with more than one range value. It is important to note that multiple domain values having the same range value does not violate the definition of a function; the key is that each individual domain value must produce a unique output.