To determine what Ronnie's data represents, we need to understand the definitions of relation and function:
1. Relation: A set of ordered pairs. In this context, the data pairs each classmate’s number of siblings with their number of pets.
2. Function: A specific type of relation where each input (number of siblings) is associated with exactly one output (number of pets). This means no two classmates with the same number of siblings should report a different number of pets.
Let's analyze the pairs given in Ronnie's survey:
- Number of siblings: 3, 1, 0, 2, 4, 1, 5, 3
- Number of pets: 4, 3, 7, 4, 6, 2, 8, 3
We can pair these up to view them as follows:
- (3, 4)
- (1, 3)
- (0, 7)
- (2, 4)
- (4, 6)
- (1, 2)
- (5, 8)
- (3, 3)
Now, examine if each number of siblings maps uniquely to a number of pets:
- The number of siblings 3 maps to both 4 and 3.
- The number of siblings 1 maps to both 3 and 2.
Since the number of siblings values of 3 and 1 do not correspond consistently to just one number of pets, this means the mapping is not unique.
Given that there are instances where a single number of siblings maps to multiple different numbers of pets, the relation is not a function.
Thus our options are narrowed down. Since every set of ordered pairs forms a relation but not all form a function, and in our case, it does not meet the criteria for being a function, we need to check if:
- The data is strictly just a relation or not valid at all. Since the inconsistent mappings indicate that it doesn't fit neatly into the category of relation or function due to contradiction in values, the proper conclusion is:
3 should map to only one value, and 1 should map to only one value. Neither happens here, invalidating both definitions.
Therefore, these inconsistencies lead us to the answer:
C. neither a relation nor a function.
