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 $-4leq xleq6$ goes from least to greatest.
$f(x)$
$x$ $g(x)$
$-4$ $57$
$-2$ $33$
$0$ $17$
$2$ $9$
$4$ $9$
$6$ $17$
$h(x)=-x^{2}-8x + 30$

Explanation:

Step1: Recall average rate - of - change formula

$\text{Average rate of change}=\frac{f(b)-f(a)}{b - a}$, where $a=-4$ and $b = 6$.

Step2: Calculate for $f(x)$

Find $f(-4)$ and $f(6)$ from the graph and use the formula.

Step3: Calculate for $g(x)$

$g(-4)=57$, $g(6)=17$, so $\frac{g(6)-g(-4)}{6-(-4)}=\frac{17 - 57}{10}=\frac{-40}{10}=-4$.

Step4: Calculate for $h(x)$

$h(-4)=-(-4)^2-8(-4)+30=-16 + 32+30=46$, $h(6)=-6^2-8\times6 + 30=-36-48 + 30=-54$. Then $\frac{h(6)-h(-4)}{6-(-4)}=\frac{-54 - 46}{10}=\frac{-100}{10}=-10$.

Step5: Order the rates

Order the average rates of change from least to greatest.

Answer:

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