Answer:
f(x) > h(x) > g(x)
Step-by-step explanation:
For the average rate of change of a function between x = a and x = b,
Average rate of change = ![\frac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
From the table given,
Average rate of change of function 'f' between x = 1 and x = 3,
Average rate of change = ![\frac{f(3)-f(1)}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%283%29-f%281%29%7D%7B3-1%7D)
= ![\frac{15-7}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7B15-7%7D%7B3-1%7D)
= 4
For the function 'g',
g(x) = 2x² - 18x
Average rate of change = ![\frac{g(3)-g(1)}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bg%283%29-g%281%29%7D%7B3-1%7D)
g(3) = 2(3)²- 18(3)
= 18 - 54
= -36
g(1) = 2(1)² - 18(1)
= 2 - 18
= -16
Therefore average rate of change = ![\frac{-36+16}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7B-36%2B16%7D%7B3-1%7D)
= -10
From the graph attached,
Average rate of change of the graph between x = 1 and x = 3,
Average rate of change = ![\frac{h(3)-h(1)}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%283%29-h%281%29%7D%7B3-1%7D)
h(3) = 7.5 [Although the graph is not clear]
h(1) = 2
Average rate of change = ![\frac{7.5-2}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7B7.5-2%7D%7B3-1%7D)
= 2.75
Therefore, order of rate of change (from greatest to the least) for the given functions will be,
f(x) > h(x) > g(x)