question given the function g(x)=x² - 9x + 18, determine the average rate of change of the function over the…

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, $a = 0$, $b = 8$, and $g(x)=x^{2}-9x + 18$.

Step2: Calculate $g(8)$

Substitute $x = 8$ into $g(x)$: $g(8)=8^{2}-9\times8 + 18=64-72 + 18=10$.

Step3: Calculate $g(0)$

Substitute $x = 0$ into $g(x)$: $g(0)=0^{2}-9\times0 + 18=18$.

Step4: Calculate the average rate of change

$\frac{g(8)-g(0)}{8 - 0}=\frac{10 - 18}{8}=\frac{-8}{8}=-1$.

Answer:

$-1$