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 (1leq xleq9) from least to greatest.
function (f(x)) graph
table for (g(x)): (\begin{array}{|c|c|}hline x&g(x)\hline - 3&74\hline1&20\hline5&10\hline9&20\hline13&74\hlineend{array}
(h(x)=-x^{2}+2x + 17)

Explanation:

Step1: Recall average rate - of - change formula

$\text{Average rate of change}=\frac{f(b)-f(a)}{b - a}$, where $a = 1$ and $b = 9$.

Step2: Calculate for $f(x)$

Read $f(1)$ and $f(9)$ from graph. Assume $f(1)=y_1$ and $f(9)=y_2$, average rate of change of $f(x)$ is $\frac{f(9)-f(1)}{9 - 1}=\frac{y_2 - y_1}{8}$.

Step3: Calculate for $g(x)$

$g(1) = 20$, $g(9)=20$, so average rate of change of $g(x)$ is $\frac{g(9)-g(1)}{9 - 1}=\frac{20 - 20}{8}=0$.

Step4: Calculate for $h(x)$

$h(x)=-x^{2}+2x + 17$, $h(1)=-1 + 2+17=18$, $h(9)=-81 + 18+17=-46$. Average rate of change of $h(x)$ is $\frac{h(9)-h(1)}{9 - 1}=\frac{-46 - 18}{8}=\frac{-64}{8}=-8$.

Answer:

$h(x),g(x),f(x)$