Final answer:
A function represented by a horizontal line remains constant and therefore does not increase over any interval. Since the function f(x) is constant between 0 and 20, there is no interval of increase. With continuous probability distributions, probabilities are derived from the areas under the function's curve rather than intervals of increase.
Step-by-step explanation:
To determine on what interval a given function is increasing, we analyze the behavior of the function with respect to its input values, which in this case are the real numbers between 0 and 20, inclusive. If the graph of the function f(x) is a horizontal line, then the function does not increase or decrease; it stays constant. Thus, for a horizontal line, there is no interval on which the function is increasing.
When discussing a continuous probability distribution, the concept of increasing does not apply in the traditional sense of a function's slope because the probability of a specific value for continuous data is zero. Instead, one looks at the probability density function and calculates probabilities based on the area under the curve. For a horizontal line which is a valid probability density function, the function would represent a uniform distribution, and probabilities are calculated based on the area within a specified interval.