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 = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
From the table given,
Average rate of change of function 'f' between x = 1 and x = 3,
Average rate of change = [tex]\frac{f(3)-f(1)}{3-1}[/tex]
= [tex]\frac{15-7}{3-1}[/tex]
= 4
For the function 'g',
g(x) = 2x² - 18x
Average rate of change = [tex]\frac{g(3)-g(1)}{3-1}[/tex]
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 = [tex]\frac{-36+16}{3-1}[/tex]
= -10
From the graph attached,
Average rate of change of the graph between x = 1 and x = 3,
Average rate of change = [tex]\frac{h(3)-h(1)}{3-1}[/tex]
h(3) = 7.5 [Although the graph is not clear]
h(1) = 2
Average rate of change = [tex]\frac{7.5-2}{3-1}[/tex]
�� = 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)
