linear
Isn this a linear function and is it discreste?
The water level of a swimming pool as it is being filled with water for 20 minutes, then stopped and filled for another 20 minutes.
The fundamental fact underpinning a linear relationship in two variables is that the ratio of the change in a first variable to the change in a second variable is constant.
If the pool level (the first variable) rises by the same amount over ANY 20 minute period (the second variable), then there is a linear relationship between time elapsed and the change in the pool level. Note that the
ratio of increase in pool level to time elapsed doesn't change whether you make your measurements over 2 minutes, 20 minutes, 40 minutes, x minutes.
Consider also that the relationship between pool level and elapsed time will not likely be linear if the pool walls rise with a slope rather than vertically.
Discrete? I am guessing you are being asked to consider the elements of the domain set (time) and of the range set (pool level). In both cases the elements are "continuous" rather then "discrete" because in theory, time can take on any value greater than 0, same with the increase in pool level. In practice however, this is not the case, every measuring device comes with a specified tolerance and hence can issue only discrete values. For example a wrist watch only gives you elapsed time in the discrete units of seconds, and ruler lines will only give you discrete differences in terms of perhaps 1/4 or 1/8 of, say, an inch.
Hmmm, is the flow of time really continuous or imperceptibly discrete, a tick, tick, tick of nano-nano seconds? Do "continuous" equations truly describe reality or only our perception of reality, like those tree branches waving across the way?
