Question

Must a function that is decreasing over a given interval always be negative over that same interval? Explain.

Answer 1

The correct answer is:
no.

Explanation:
For a function to be decreasing over an interval, the value of the function, f(x), must decrease as x increases. This does not, however, mean that the values of the function are negative. The function could have a positive range while still decreasing (becoming smaller positive numbers as x increase).

Answer 2

Answer:

The function may not be negative if the function is decreasing over a given interval.

Step-by-step explanation:

Let the function be f(x)

If the function f(x) is decreasing then it implies that the value of the function f(x) is decreasing with the increase in value of x over the given interval.

A function f(x) is said to be decreasing if the derivative of the function f'(x) is negative. This does not implies that the function is negative.

Hence, The function may not be negative if the function is decreasing over a given interval.