To determine what value can be added to the mapping diagram so that it no longer represents a function, we need to understand the definition of a function.
A function is defined as a relation in which each element from the domain is associated with exactly one element in the range. This means that no two different pairs in the domain can map to the same value in the range.
From the mappings you've provided, the current associations are:
- 10 → 9
- 1 → 5
- 6 → (not clearly associated yet)
The range values currently represented by the domain values are:
- For 10, the range is 9.
- For 1, the range is 5.
- For 6, it hasn’t been paired yet.
To make this mapping not a function, we can add a mapping for the domain value 6 that would cause it to map to a value that is already used by another domain value, specifically to 5 or 9 (the values already represented in the range).
For example, if we add the association 6 → 5, then both 1 and 6 will be mapping to 5, making it so that the element 5 in the range is associated with two different elements in the domain (1 and 6), which violates the definition of a function.
Thus, adding the mapping:
- 6 → 5 will ensure that the relation is NOT a function.
Alternatively, adding:
- 6 → 9 would also create the same problem.
Either of these additions will make the relation not a function.
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