Step-by-step explanation:
To find the average rates of change for each function on the interval \([3, 5]\), we use the formula:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
Where \(a = 3\) and \(b = 5\).
1. For \(f(x)\):
\[
\text{Average Rate of Change} = \frac{f(5) - f(3)}{5 - 3} = \frac{8 - 10}{2} = -1
\]
2. For \(g(x)\):
\[
\text{Average Rate of Change} = \frac{g(5) - g(3)}{5 - 3} = \frac{8 - 10}{2} = -1
\]
3. For \(h(x)\):
\[
\text{Average Rate of Change} = \frac{h(5) - h(3)}{5 - 3} = \frac{8 - 10}{2} = -1
\]
So, the average rates of change for all three functions are the same. Therefore, the order of the functions according to their average rates of change on the interval \([3, 5]\) is the same for all of them.