Select the correct answer.
Nate 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 these results is below.
Which of the following does Ronnie's data represent?
A. Not a function
B. Neither a relation nor a function
C. A function
D. A relation only
Answer (2)
Represent the given data as ordered pairs.
Determine that the data represents a relation because it is a set of ordered pairs.
Check if the data represents a function by looking for repeated inputs with different outputs.
Conclude that the data represents a relation only because there are repeated inputs with different outputs. The answer is a re l a t i o n o n l y .
Explanation
Understanding the Problem Rionnie surveyed eight classmates about the number of siblings and pets they have. The data is presented in a table with the number of siblings and pets for each classmate. We need to determine whether this data represents a relation, a function, both, or neither.
Representing the Data Let's represent the data as a set of ordered pairs (number of siblings, number of pets): (3, 4), (1, 3), (0, 7), (2, 4), (4, 6), (1, 2), (5, 8), (3, 3).
Checking for a Relation A relation is simply a set of ordered pairs. Since we have a set of ordered pairs, the data represents a relation.
Checking for a Function A function is a relation where each input (number of siblings) has only one output (number of pets). To determine if the data represents a function, we need to check if there are any repeated inputs with different outputs. Looking at the data, we see that the input '3' appears twice, once with an output of '4' and once with an output of '3'. Similarly, the input '1' appears twice, once with an output of '3' and once with an output of '2'. Since there are repeated inputs with different outputs, the data does not represent a function.
Conclusion Since the data represents a relation but not a function, the correct answer is that it represents a relation only.
Examples
Understanding relations and functions is crucial in many real-world scenarios. For instance, consider a vending machine where you input a code (the input) and receive a specific item (the output). If each code corresponds to only one item, it's a function. However, if one code could potentially dispense different items at different times due to malfunctions, it's a relation but not a function. Similarly, in databases, relations define how data is connected, and understanding functional dependencies helps ensure data integrity and consistency.
Ronnie's data is a relation because it consists of ordered pairs representing the relationship between the number of siblings and pets. However, it is not a function since some inputs (number of siblings) lead to multiple outputs (number of pets). The correct option is D, a relation only.
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