Final answer:
The most plausible interval where the function f(x) is negative, based on the conventional representation of intervals and the typical behavior of functions, is option d. (-6, -8).
Step-by-step explanation:
The question asks to identify the interval over which a function f(x) is negative. Without the specific function provided, we must rely on typical characteristics of mathematical functions and their graphs. First, let's consider the nature of intervals. An interval where a function is negative is a range of x-values for which the corresponding y-values (or function values f(x)) are less than zero.
If we look through the options given: a. (-8, -16), b. (0, 16), c. (2, 32), d. (-6, -8), we are looking for an interval where it would make sense for the function to be negative. Given that negative x-values often correspond to negative y-values on a typical graph (though it is not a strict rule), the most likely answer is the one that contains negative x-values exclusively. This reason eliminates options b and c which contain positive numbers. Now between options a and d, d gives an interval where the smaller number comes first, which is conventional in mathematics. Hence, option a. (-8, -16) is incorrect while option d. (-6, -8) seems plausible.