The only interval with a negative rate of change is the last one:
[1, 2.5]
When the rate of change is negative?
For an interval (a, b) and a function f(x), the rate of change is defined as:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
So the rate of change is only negative when the function evaluated on the first value of the interval is larger than the function evaluated in the second one.
For example, on the interval [1, 2.5} we can see that:
f(1) = 3
f(2.5) = -1
Then on this interval, the rate of change will be negative, meaning that this is the correct option.
If you want to learn more about rates of change, you can read:
https://brainly.com/question/8728504
