Final answer:
The relation (length, volume) of a swimming pool is a function because each specific length corresponds to a specific volume. However, the relation (volume, length) is not a function as the same volume can correspond to different lengths due to varying shapes and sizes.
Step-by-step explanation:
In considering the groups, the length of a swimming pool and the liquid volume of the pool, we assess whether each can be considered functions of the other. The concept of a function in mathematics deals with a relationship between two sets where each element in the first set is associated with exactly one element in the second set. The length of a swimming pool is a one-dimensional measure and can determine the volume since the volume can be found by knowing the length along with width and depth (assuming a standard geometric shape). Therefore, for every specific length, there is a corresponding volume, making the relation (length, volume) a function. However, the opposite is not true; a particular volume does not correspond to a unique length since multiple combinations of length, width, and depth can result in the same volume. Thus, the relation (volume, length) is not a function.