Question

The functions f(x), g(x), and h(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≤x≤7 goes from least to greates

Answer 1

Given

Function f(x) , g(x) and h(x)

Find

Order of the function according to average rate of change

Step-by-step explanation

Average rate of change can be given by

`(f(b)-f(a))/(b-a)`
`3\leq x\leq7`

for f(x)

`\begin{gathered} (f(7)-f(3))/(7-3) \\ \\ (-10-(-8))/(4) \\ \\ -(2)/(4) \\ \\ -(1)/(2) \end{gathered}`

for g(x)

`\begin{gathered} (g(7)-g(3))/(7-3) \\ \\ (7-(27))/(4) \\ \\ -(20)/(4) \\ \\ -5 \end{gathered}`

for h(x)

`\begin{gathered} (h(7)-h(3))/(7-3) \\ \\ (60-24)/(4) \\ \\ (36)/(4) \\ 9 \end{gathered}`

Final Answer

least to greatest = g(x) , f(x) . h(x)

correct option is 2.