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Ronnie took a survey of eight of his classmates about the number of siblings they have and the number of pets they have. A table of his results is below.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
\# of Siblings & 3 & 1 & 0 & 2 & 4 & 1 & 5 & 3 \\
\hline
\# of Pets & 4 & 3 & 7 & 4 & 6 & 2 & 8 & 3 \\
\hline
\end{tabular}

Which of the following does Ronnie's data represent?

A. Both a function and a relation
B. Neither a relation nor a function
C. A function only
D. A relation only

Sagot :

GinnyAnswer
To determine which of the options Ronnie's data represents, let's first understand the definitions of a function and a relation.

### Relation
A relation is any set of ordered pairs. In this context, Ronnie's data creates a set of ordered pairs where each pair consists of the number of siblings and the corresponding number of pets for each classmate.

### Function
A function is a specific type of relation in which each input (number of siblings) is associated with exactly one output (number of pets). This means that no two ordered pairs can have the same first element (number of siblings) with different second elements (number of pets).

Now, let's analyze the data given in the problem:

[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]

Based on this data, we can create the following ordered pairs:
[tex]\[ (3, 4), (1, 3), (0, 7), (2, 4), (4, 6), (1, 2), (5, 8), and (3, 3) \][/tex]

To determine if this data represents a function, we need to check whether each unique number of siblings maps to exactly one number of pets.

### Checking the pairs:
- The first pair (3, 4) maps 3 siblings to 4 pets.
- The second pair (1, 3) maps 1 sibling to 3 pets.
- The third pair (0, 7) maps 0 siblings to 7 pets.
- The fourth pair (2, 4) maps 2 siblings to 4 pets.
- The fifth pair (4, 6) maps 4 siblings to 6 pets.
- The sixth pair (1, 2) maps 1 sibling to 2 pets. This conflicts with the second pair, which maps 1 sibling to 3 pets.
- The seventh pair (5, 8) maps 5 siblings to 8 pets.
- The eighth pair (3, 3) maps 3 siblings to 3 pets. This conflicts with the first pair, which maps 3 siblings to 4 pets.

Since we have multiple instances where the same number of siblings maps to different numbers of pets (e.g., (1, 3) and (1, 2), as well as (3, 4) and (3, 3)), this set of data does not satisfy the definition of a function.

Therefore, Ronnie's data represents a relation but not a function.

So, the correct answer is:
D. a relation only
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