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.

Question

# of Siblings 3 1 0 2 4 1 5 3
# of Pets 4 3 7 4 6 2 8 3

Which of the following does Ronnie's data represent?
A.
a function only
B.
both a function and a relation
C.
a relation only
D.
neither a relation nor a function

Answer 1

To determine what Ronnie's data represents, we must first understand the definitions of a relation and a function:

• A relation is any set of ordered pairs.
• A function is a specific type of relation where each input (in this case, the number of siblings) is associated with exactly one output (the number of pets).

In Ronnie's data, we will analyze the number of siblings and the corresponding number of pets:

• 3 siblings -> 4 pets
• 1 sibling -> 3 pets
• 0 siblings -> 7 pets
• 2 siblings -> 4 pets
• 4 siblings -> 6 pets
• 1 sibling -> 2 pets
• 5 siblings -> 8 pets
• 3 siblings -> 3 pets

Now, let's check if any number of siblings (input) corresponds to more than one number of pets (output):

• 1 sibling corresponds to both 3 pets and 2 pets.
• 3 siblings corresponds to both 4 pets and 3 pets.

Since the same input (number of siblings) is linked to different outputs (number of pets), the data does not qualify as a function.

However, it still represents a relation because it is a set of ordered pairs.

Given this analysis, the correct answer is:

C. a relation only