Final answer:
The number of gallons of water in the bathtub is a function of time because at each moment, there is exactly one measure of water in the bathtub, making option A correct.
Step-by-step explanation:
The number of gallons of water in the bathtub over time is indeed a function of time, assuming the water level changes as time passes. In answering the question if it is a function, we should consider whether a single time value is paired with more than one value of gallons. According to option A, in the context of a bathtub being filled or drained, at any given time, there would be an exact measure of gallons in the bathtub. Hence, option A, which states that each value of time is paired with exactly one number of gallons, is correct. The remaining options are not relevant to defining a function in the context described; the boundedness (option B) does not imply functionhood, and options C and D suggest misunderstandings of how a function is defined.