Final answer:
This question involves evaluating constant functions within an interval, identifying properties of specific functions, and understanding uniform probability distributions and their probabilities over given intervals.
Step-by-step explanation:
The question pertains to function evaluation and understanding probability distributions within specified intervals. In one instance, we're given a function f(x) that is a horizontal line from 0 ≤ x ≤ 20 and is restricted to the portion between x = 0 and x = 20, inclusive. This would imply that for any value of x in that range, f(x) would be constant.
Regarding function options at x = 3, a function with a positive value and positive slope that decreases as x increases could be represented by y = x² since the slope (∂y/∂x = 2x) is positive and decreases as x increases beyond 3.
Considering continuous probability functions, f(x) equal to a constant within a range implies a uniform distribution. So, the probability P(0 < x < 12) is 1. Also, for P(x > 3) where f(x) is restricted to 1 ≤ x ≤ 4, the probability is the area under the curve from x = 3 to x = 4, which would be a simple fraction of the overall area under the probability function.