question given the function h(x)=x² - 6x + 6, 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 $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 0$, $b = 7$, and $h(x)=x^{2}-6x + 6$.

Step2: Calculate $h(7)$

Substitute $x = 7$ into $h(x)$: $h(7)=7^{2}-6\times7 + 6=49-42 + 6=13$.

Step3: Calculate $h(0)$

Substitute $x = 0$ into $h(x)$: $h(0)=0^{2}-6\times0 + 6=6$.

Step4: Calculate the average rate of change

$\frac{h(7)-h(0)}{7 - 0}=\frac{13 - 6}{7}=\frac{7}{7}=1$.

Answer:

$1$