Question
Look at this mapping diagram:
Domain
Range
3
–9
12
5
11
17
18
11
4
Is this relation a function? yes or no
Domain
Range
3
–9
12
5
11
17
18
11
4
Is this relation a function? yes or no
Answers
GPT-4o mini
To determine if the relation represented by the mapping diagram is a function, we need to check if each element in the domain maps to exactly one element in the range. In other words, no element in the domain should map to more than one element in the range.
From the mapping diagram you provided, we can see the following mappings:
- 3 maps to –9
- 12 maps to 5
- 11 maps to 17
- 18 maps to 11
- 4 maps to an unspecified element (not given)
Without the explicit mapping for 4, we cannot fully assess whether this relation meets the definition of a function. However, based on the mappings provided:
If the elements 3, 12, 11, 18, and 4 each map to a unique element in the range (not repeating any), then this relation can be considered a function.
From what's shown, we see:
- 3 → –9 (unique)
- 12 → 5 (unique)
- 11 → 17 (unique)
- 18 → 11 (unique)
As long as 4 maps to something unique and does not map to an element already represented in the range, this relation would be a function.
However, if element "4" maps to any of the already-mapped range values (–9, 5, 17, 11), then the relation would not be a function because you would have one domain element (4) mapping to more than one range element.
If there is no overlap in range mappings for 4 or if you assume it simply has its own mapping, then the answer is **yes, this is a function.** If 4 maps to an existing range element, the answer could be **no, this is not a function.**
Since we don't know how 4 maps, the answer would depend on that missing information.
From the mapping diagram you provided, we can see the following mappings:
- 3 maps to –9
- 12 maps to 5
- 11 maps to 17
- 18 maps to 11
- 4 maps to an unspecified element (not given)
Without the explicit mapping for 4, we cannot fully assess whether this relation meets the definition of a function. However, based on the mappings provided:
If the elements 3, 12, 11, 18, and 4 each map to a unique element in the range (not repeating any), then this relation can be considered a function.
From what's shown, we see:
- 3 → –9 (unique)
- 12 → 5 (unique)
- 11 → 17 (unique)
- 18 → 11 (unique)
As long as 4 maps to something unique and does not map to an element already represented in the range, this relation would be a function.
However, if element "4" maps to any of the already-mapped range values (–9, 5, 17, 11), then the relation would not be a function because you would have one domain element (4) mapping to more than one range element.
If there is no overlap in range mappings for 4 or if you assume it simply has its own mapping, then the answer is **yes, this is a function.** If 4 maps to an existing range element, the answer could be **no, this is not a function.**
Since we don't know how 4 maps, the answer would depend on that missing information.