Final answer:
The details given in the examples do not correspond to a function with a positive slope that decreases as x increases. Instead, they describe various types of functions, including horizontal lines and probability functions, as well as the relationship between variables with a constant product.
Step-by-step explanation:
To answer the question regarding which function could correspond to f(x) when f(x) has a positive value at x = 3 with a positive slope that decreases in magnitude with increasing x, we must consider the characteristics of the given options: y = 13x and y = x². Option (a) y = 13x represents a straight line with a constant slope, which does not fit the description, as the slope does not decrease. On the other hand, option (b) y = x² represents a parabola, which starts with a slope of 0 at x = 0 and increases as x increases; however, since f(x) must have a decreasing slope, not an increasing one, neither of these functions match the description given.
In the case of the horizontal function f(x) = 20, which is restricted to the domain 0 ≤ x ≤ 20, the graph would be a horizontal line at the y-value of 20 from x = 0 to x = 20. For the function f(x) = 8, restricted within 0 ≤ x ≤ 8, it can also be represented by a horizontal line at the y-value of 8 from x = 0 to x = 8, and the probability P(2.5 < x < 7.5) can be calculated using the properties of a uniform distribution over the interval [0,8].
For the continuous probability function f(x), the probability P(x > 3) is calculated by integrating the probability function from x = 3 to the upper bound of its domain. Finally, regarding the statement about the product of f multiplied by another variable being constant, it highlights the inverse relationship between two quantities: when one increases, the other must decrease to maintain a constant product.