Question

Which of the following statements correctly describes the behavior of a function over the given interval?

A. The function is positive over the interval [x/3, [infinity]].
B. The function is negative over the interval [x/2, [infinity]].
C. The function is positive over the interval (-[infinity], x/2].
D. The function is negative over the interval [x/3, x/2].

Answer 1

The correct statement that describes the behavior of the function is option D - The function is negative over the interval [x/3, x/2].

Step-by-step explanation:

The correct statement that describes the behavior of the function in question is option D. The function is negative over the interval [x/3, x/2].

To understand why this is the correct option, let's analyze the given information:

• The function has a positive value at x = 3, which eliminates option B.
• It has a positive slope that is decreasing in magnitude with increasing x, which eliminates option A.
• Option C is incorrect because it states that the function is positive, but we have already determined that it is negative.

Considering these facts, option D is the only statement that correctly describes the behavior of the function over the given interval.