Answer :
Let's analyze the relationship between the number of siblings and the number of pets based on the given data. Here's the table for better clarity:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \# \mathrm{of~Siblings} & 3 & 1 & 0 & 2 & 4 & 1 & 5 & 3 \\ \hline \# \mathrm{of~Pets} & 4 & 3 & 7 & 4 & 6 & 2 & 8 & 3 \\ \hline \end{array} \][/tex]
### Step-by-Step Analysis:
1. List the pairs of (siblings, pets):
[tex]\[ (3, 4), (1, 3), (0, 7), (2, 4), (4, 6), (1, 2), (5, 8), (3, 3) \][/tex]
2. Group by the number of siblings to see if each sibling count maps to a unique number of pets:
- 3 siblings: [4, 3]
- 1 sibling: [3, 2]
- 0 siblings: [7]
- 2 siblings: [4]
- 4 siblings: [6]
- 5 siblings: [8]
3. Check for a function:
- A function requires that each input (number of siblings) maps to exactly one output (number of pets). In other words, each sibling count should have exactly one corresponding pet count.
- In the given pairs, we see that:
- 3 siblings map to both 4 pets and 3 pets.
- 1 sibling maps to both 3 pets and 2 pets.
Since the number of siblings 3 and 1 both map to more than one number of pets, this violates the definition of a function.
### Conclusion:
- The data does not represent a function since there are instances where the same number of siblings maps to different numbers of pets.
- The data does represent a relation because a relation is simply a set of ordered pairs without the restriction that each input must map to exactly one output.
Therefore, the correct answer is:
```
D. a relation only
```
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \# \mathrm{of~Siblings} & 3 & 1 & 0 & 2 & 4 & 1 & 5 & 3 \\ \hline \# \mathrm{of~Pets} & 4 & 3 & 7 & 4 & 6 & 2 & 8 & 3 \\ \hline \end{array} \][/tex]
### Step-by-Step Analysis:
1. List the pairs of (siblings, pets):
[tex]\[ (3, 4), (1, 3), (0, 7), (2, 4), (4, 6), (1, 2), (5, 8), (3, 3) \][/tex]
2. Group by the number of siblings to see if each sibling count maps to a unique number of pets:
- 3 siblings: [4, 3]
- 1 sibling: [3, 2]
- 0 siblings: [7]
- 2 siblings: [4]
- 4 siblings: [6]
- 5 siblings: [8]
3. Check for a function:
- A function requires that each input (number of siblings) maps to exactly one output (number of pets). In other words, each sibling count should have exactly one corresponding pet count.
- In the given pairs, we see that:
- 3 siblings map to both 4 pets and 3 pets.
- 1 sibling maps to both 3 pets and 2 pets.
Since the number of siblings 3 and 1 both map to more than one number of pets, this violates the definition of a function.
### Conclusion:
- The data does not represent a function since there are instances where the same number of siblings maps to different numbers of pets.
- The data does represent a relation because a relation is simply a set of ordered pairs without the restriction that each input must map to exactly one output.
Therefore, the correct answer is:
```
D. a relation only
```
