Final answer:
Each student's unique identification number paired with their grade level is indeed a function, since every identification number (input) is associated with one grade level (output). The correct answer is option a. Yes, it is a function.
Step-by-step explanation:
The correct answer is option a. Yes, it is a function. A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. In this case, each student's unique identification number is an input that would be paired with exactly one grade level, the output.
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of outputs (called the range), such that each input is related to exactly one output. In the given scenario, each student's unique identification number is paired with their grade level. However, it is possible for multiple students to have the same grade level.
For example, if we have two students with the same grade level, let's say 9th grade, then their unique identification numbers would be paired with the same output. This violates the definition of a function, as one input (unique identification number) is related to multiple outputs (grade level).
Therefore, the given scenario is not a function.
There are no scenarios where a unique identification number would be paired with more than one grade level in the context provided. Therefore, the pairing of student identification numbers with their respective grade levels constitutes a function because it adheres to the definition of a function in mathematical terms.