Final Answer:
Yes, the relation is a function because each friend corresponds to a unique height. Every friend has a distinct height value, and no two friends share the same height.
Step-by-step explanation:
In the context of functions, a relation is considered a function if each input (in this case, each friend's name) is associated with a unique output (each friend's height). In the provided data, each friend has a specific height value, and no two friends share the same height. This one-to-one correspondence fulfills the criteria for a function.
A function is essentially a special type of relation where each input is paired with exactly one output. In Bailey's record, the friends' names serve as inputs, and the corresponding heights serve as unique outputs, establishing a functional relationship.
The uniqueness of the height values is crucial in determining whether the relation is a function. If there were repeated height values for different friends, it would violate the one-to-one correspondence required for a function. However, in this case, each friend has a distinct height, affirming that the relation is indeed a function. This understanding is foundational in mathematical reasoning and lays the groundwork for more advanced concepts in algebra and calculus.
In conclusion, the relation of Bailey's friends' heights satisfies the conditions for a function. The unique correspondence between each friend and their height values affirms the functional nature of the data set, providing a clear example of a one-to-one relation.