question given the function g(x)=-x² - 6x + 14, determine the average rate of change of the function over…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a=-4$, $b = 0$, and $g(x)=-x^{2}-6x + 14$.

Step2: Calculate $g(0)$

Substitute $x = 0$ into $g(x)$: $g(0)=-(0)^{2}-6(0)+14=14$

Step3: Calculate $g(-4)$

Substitute $x=-4$ into $g(x)$: $g(-4)=-(-4)^{2}-6(-4)+14=-16 + 24+14=22$

Step4: Calculate the average rate of change

Using the formula $\frac{g(b)-g(a)}{b - a}$, we have $\frac{g(0)-g(-4)}{0-(-4)}=\frac{14 - 22}{4}=\frac{-8}{4}=-2$

Answer:

$-2$