Question

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

Answer 1

For a function to be decreasing over an interval, the outputs are getting smaller as the inputs of the function are getting larger.

The outputs of a decreasing interval could be positive or negative.

For a function to be negative over an interval, the outputs must be negative, while the inputs could be positive or negative.

Explanation:

Answer 2

No. The sign of a function is not related with the fact that it is growing of decreasing.

If the function in the decreasing in the interval (a,b) it means that f(b) < f(a), but yet both f(b) and f(a) may be positive.

For example imagin the function y = - x. It is a straight line and it is decreasing for any interval that you take; this is (-∞, ∞).

If you take the interval (- ∞, 0) the function is decreasing but the values are positive. If you take the interval (0, ∞) the function is decreasing and the values are negative.