Can someone explain this or answer?

Ok so you are correct that x is input and y is output
the
you could be talking about a function in general or a kind of function normally used called a one-to-one function which I will assume you are talikning about

one-to-one funciton has that for every input, there is only 1 output, ie, x never repeats with a diffent y
example
(1,2), (2,2) is a function since x didn't repeat 
(1,2), (1,3) is not since  x repeats with a different y

points given are

(-5,1),(-3,-2), (3,0),(1,1),(2,0),(6,4)(8,-2),(8,7)
we see that the points (8,-2) and (8,7) make it not a function since it is the same input (8) that gives 2 different outputs

professor octavious is wrong since 8 repeats