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

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.