Question

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

Answer 1

Hello,

No, a function that is decreasing over a given interval doesn't always have to be negative over that same interval. 

The function can be positive over the whole interval if it is positive at the right hand end.

Faith xoxo

Answer 2

Answer:

It is not must for a function to be negative on the same interval, if it is decreasing on a given interval.

Step-by-step explanation:

Please find the attachment.

We are asked to determine is it must for a function that that is decreasing over a given interval always be negative over that same interval.

We know that a function is known as decreasing over an interval, when the value of function is decreasing as x increases.

The value of function is negative, when function is below x-axis.

It is not necessary that a function must be negative if it is decreasing on a given interval. For example function $f(x)=4-x^2$.  We can see that our function is decreasing on $[0,\infty]$, but is positive on interval $[0,2]$.

Therefore, it is not must for a function to be negative on the same interval, if it is decreasing on a given interval.