# Need to determine whether the relation is a function or not

1
by mrambabu1600
you could write the question directly, instead of enclosing in a document. please do that next time. it is more convenient to see question directly.

2014-10-18T20:26:19+05:30

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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 }

thanx n u r welcom