In order for a mapping diagram to show a relation that is NOT a function, at least one input (domain) must be mapped to more than one output (range).
Based on the mapping you provided:
- Domain: 10 maps to 9
- Domain: 1 maps to 5
- Domain: 6 maps to a value that is not provided.
The current mappings suggest that:
- 10 → 9 (one unique mapping)
- 1 → 5 (one unique mapping)
- 6 → (unknown, but presumably maps to one unique value)
Now, let's analyze the choices: 9, 5, 6, and 2.
To create a situation that is NOT a function, we need to choose a value from the provided options and have it map back to either 10 or 1 (since these have already been mapped to unique values).
Thus:
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If we add an output value of 9 for the input 6, we have:
- 6 → 9 Then 9 is no longer unique, as 10 also maps to 9, creating a situation where one input (both 10 and 6) maps to the same output (9) — but this scenario does not break the function condition.
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If we add an output of 5 for the input 6:
- 6 → 5 Now both 1 and 6 would share the output of 5, leading to 1 and 6 mapping to the non-unique output of 5—a violation of the function rule.
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If we add an output of 6 (where 6 was originally just an input):
- 6 → 6 This does not impact the uniqueness of the existing mappings.
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If we add an output of 2 for the input 6:
- 6 → 2 This does not cause any violations.
From this reasoning, if we add 5 to the output for input 6, it would create a mapping where both 1 and 6 point to the same output of 5, thus the relation would no longer be a function.
So, the value that needs to be added to make the mapping diagram show a relation that is NOT a function is 5.