Question

A student thinks that the relation {(2,1),(3-2),(4,5),(5,-2) is not a function because the two values in the domain have the same range value..What is the student's error?

Answer 1

the student has it backwards, we are allowed to have repeated y values
think of y=3, then y is a function and (1,3),(2,3),(3,3) are all points on the line

but if you have 1 x value mapping to two different y values then you have broken the well defined property of a function

i.e.
\(a=b\implies f(a)=f(b)\)