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The functions f, of, xf(x), g, of, xg(x), and h, of, xh(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 3, is less than or equal to, x, is less than or equal to, 53≤x≤5 goes from least to greatest.

f, of, x

f(x)

x

y

xx g, of, xg(x)

11 2020

22 1414

33 1010

44 88

55 88

Verified Answer :

yuzhong885

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.

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