
The above function is to be used if the value of x is between 0 and 8. On the other hand, the function to be used when x ≥ 8 is -5x + 11.
Since the interval to be checked is from 2 to 7, we will be using the first function which is -2x + 4.
To determine the rate of change between those intervals, we have the formula below:

Let's solve f(x₂) first. Our x₂ = 7. Let's substitute the function above with x = 7.

Let's solve f(x₁) first. Our x₁ = 2. Let's substitute the function above with x = 2.

So, we now have the value of f(x₂) = -10, and f(x₁) = 0. Let's use these values to the formula of the rate of change above.

Since the rate of change is a negative number, the function is decreasing over the interval [2, 7].