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

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 .  We can see that our function is decreasing on , but is positive on interval .

Therefore, 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:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.