II. Direction: Relations Expressed as Mappings
Express the following relations as a mapping, state the domain and range, then determine if it is a function.
6. {(-2,-1), (0,3), (5,4), (-2,3)}
Domain:
Range:
Function:
7. {(-1,5), (0,3), (2,3), (3,1)}
Domain:
Range:
Function:
Answer (1)
Let's examine each relation one by one.
Relation: {(-2,-1), (0,3), (5,4), (-2,3)}
Mapping : Each pair in the relation can be written as a mapping from each first element (the domain) to the second element (the range). Here’s how it looks:
-2 maps to -1 and 3
0 maps to 3
5 maps to 4
Domain : The domain is the set of all first elements of the pairs. So, the domain is {-2, 0, 5}.
Range : The range is the set of all second elements of the pairs. So, the range is {-1, 3, 4}.
Function : A relation is a function if each element of the domain is associated with exactly one element of the range. Since -2 is paired with both -1 and 3, this relation is not a function .
Relation: {(-1,5), (0,3), (2,3), (3,1)}
Mapping : Let’s list the mappings:
-1 maps to 5
0 maps to 3
2 maps to 3
3 maps to 1
Domain : The domain is {-1, 0, 2, 3}.
Range : The range is {5, 3, 1}.
Function : This relation is a function because every element in the domain is linked to exactly one element in the range. Even though 0 and 2 both map to 3, it doesn’t affect the definition of a function. Each input has a single output, so it is a valid function.
