Rule:

Make a list of all first coordinates
If the list contains any number more than once it is NOT a function
If the list contains each number once only, it is a function.

Note: [It does not matter whether any of the second coordinates are 
the same or not, only the first coordinates matter.]

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(1,2)(3,4)(5,6)(3,-4)

That one is not a function because the list of first coordinates 1,3,5,3
contains 3 more than once, in this case twice.

(8,4)(4,3)(2,2)(8,1)

That one is not a function because the list of first coordinates 8,4,2,8,
contains 8 more than once, in this case twice.

(2,5)(3,10)(4,15)(5,20)

That one is a function because the list of first coordinates 2,3,4,5, does
not contain the same number twice.

(2,4)(2,3)(2,1)(2,0)

That one is not a function because the list of first coordinates 2,2,2,2,
contains 2 more than once, in this case four times.

Edwin