To determine what Ronnie's data represents, let's first review the definitions of a function and a relation.
1. Relation: In mathematics, a relation is simply a set of ordered pairs. Each pair consists of two related values: in this case, the number of siblings and the number of pets. Any set of data can be considered a relation as long as it groups pairs of related values together.
2. Function: A function is a specific type of relation. For each input (the first element in the pair, which is the number of siblings here), there must be exactly one output (the second element in the pair, which is the number of pets). In other words, no two ordered pairs can have the same first element (number of siblings) but different second elements (number of pets).
Let's analyze the given data:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
\# \text{ of Siblings} & 3 & 1 & 0 & 2 & 4 & 1 & 5 & 3 \\
\hline
\# \text{ of Pets} & 4 & 3 & 7 & 4 & 6 & 2 & 8 & 3 \\
\hline
\end{array}
\][/tex]
First, we note that the data indeed represents a relation because we have pairs of values: (3, 4), (1, 3), (0, 7), (2, 4), (4, 6), (1, 2), (5, 8), and (3, 3).
To determine if this relation is also a function, we check if each number of siblings maps to exactly one number of pets:
- Siblings = 3 maps to Pets = 4
- Siblings = 1 maps to Pets = 3
- Siblings = 0 maps to Pets = 7
- Siblings = 2 maps to Pets = 4
- Siblings = 4 maps to Pets = 6
- Siblings = 1 maps to Pets = 2
- Siblings = 5 maps to Pets = 8
- Siblings = 3 maps to Pets = 3
We can see that the number of siblings 3 maps to both 4 and 3. Similarly, the number of siblings 1 maps to both 3 and 2. This violates the definition of a function, where each input should map to a single output.
Given this information, Ronnie's data does not represent a function, but it does represent a relation.
Thus, the correct answer is:
C. a relation only
