To determine what Ronnic's data represents, we need to analyze the relationship between the number of siblings and the number of pets for each of his classmates.
First, let's understand the concepts:
1. Relation: A relation is a set of ordered pairs. Here, each pair consists of the number of siblings and the corresponding number of pets for each classmate.
2. Function: A function is a specific type of relation where each input (number of siblings) corresponds to exactly one output (number of pets). In other words, no two different classmates can have the same number of siblings if the data is to represent a function.
From the given data:
- Number of siblings: [tex]\(3, 1, 0, 2, 4, 1, 5, 3\)[/tex]
- Number of pets: [tex]\(4, 3, 7, 4, 6, 2, 8, 3\)[/tex]
Let’s list the ordered pairs:
[tex]\[
(3, 4), (1, 3), (0, 7), (2, 4), (4, 6), (1, 2), (5, 8), (3, 3)
\][/tex]
Now let’s check if each number of siblings corresponds to exactly one number of pets:
- For 3 siblings: 4 pets and 3 pets (two different outputs for the same input, violates function criteria)
- For 1 sibling: 3 pets and 2 pets (two different outputs for the same input, violates function criteria)
Since there are duplicate numbers of siblings (3 and 1) that correspond to different numbers of pets, this set of data cannot represent a function.
However, it still represents a relation, because it’s a set of ordered pairs.
Therefore, the correct answer is:
B. a relation only
