To solve this question, we need to analyze if the situation represents a relation, a function, both, or neither.
First, let's define the terms:
- Relation: Any set of ordered pairs (x, y).
- Function: A specific type of relation where each input (x-value) corresponds to exactly one output (y-value).
In the given problem, a particular strain of common bacteria replicates itself every 14 minutes.
This means:
- We can consider the input (x) to be the time in minutes.
- The output (y) would be the amount of bacteria.
Now let’s consider the scenario carefully:
### Relation:
Every set of ordered pairs where the first element (time) maps to the second element (amount of bacteria) forms a relation. In this situation, having the time elapsed (every 14 minutes) and the amount of bacteria at that particular time forms an ordered pair, so this does make it a relation.
### Function:
In order to be classified as a function, each input (time in minutes) must correspond to exactly one output (amount of bacteria). Given that the bacteria replicates at exact 14-minute intervals, there is a unique amount of bacteria corresponding to each 14-minute increment. This means every specific time elapse will have a unique number of bacteria, fitting the definition of a function as well.
Therefore, the scenario where the bacteria replicates itself every 14 minutes not only forms a relation but also fits the criteria to be considered a function. However, since the question asks for what the situation represents clearly and individually:
The correct choice for what the situation specifically represents is:
- D. a function only
This is because while it is both a relation and a function, the most specific classification according to the options provided is "a function only."
