Final answer:
The interval over which the function f(x) is negative would be (-8, -2) if f(x) represents a horizontal line at a negative value.
Step-by-step explanation:
To determine which interval could be the entire interval over which the function f(x) is negative, we need to analyze the descriptions of f(x) given in the options and match it with the provided scenarios. In one of the scenarios, we see that at x = 3, a function has a positive value, and its slope is positive but decreasing. The descriptions of f(x) provided in the options suggest different behaviors: a straight line with a negative slope, a straight line with a positive slope, a horizontal line at a negative value, and a horizontal line at a positive value. The horizontal line at a negative value is the only description amongst the options that guarantees that f(x) would be negative for the entire range of x values. Given that we know f(x) is restricted between x=0 and x=20, the interval (-8,-2) will obviously be negative if f(x) represents a horizontal line at a negative value.