Question

Need to determine whether the relation is a function or not

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Answer 1

I assume we are talking about relation between x and y : a relation on  R --> R 
y = f(x) is a function or not.

a)   y = f (x ) = -15
         This is a many to one function.  It is a constant function. Each value of x ∈ R (real numbers) maps to -15.   Domain is R and Range is { -15 }.

b)   x  = 5   relation could be   = { ( 5, 1), (5, 0) , (5, 9999), (5, -098) }
      Here y can be any value.  It means one value of x is mapping onto multiple values of y or F.  It is not a function, in the strict sense of a function.
       Some times it is referred to as a multi-valued function.

c)   Relation = { (1, 0 ) , (1, 4 ) ,  (-1, 1 ) } 
 
          Here x =1 is mapping to 0 and 4.  So it is not a function.      

d)   Relation = {  ( 6, 3), (5, -2 ) , (2, 3 ) } 

                 Here each value of x has a unique and one value of y.  So it is a function with domain = { 6, 5, 2 } and  range = { 3, -2 }