given the function h(x)=x² - 7x + 9, determine the average rate of change of the function over the interval…

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, $a=-1$, $b = 10$, and $h(x)=x^{2}-7x + 9$.

Step2: Calculate $h(a)$

Substitute $x=-1$ into $h(x)$: $h(-1)=(-1)^{2}-7\times(-1)+9=1 + 7+9=17$.

Step3: Calculate $h(b)$

Substitute $x = 10$ into $h(x)$: $h(10)=10^{2}-7\times10 + 9=100-70 + 9=39$.

Step4: Calculate the average rate of change

Substitute $h(-1)=17$, $h(10)=39$, $a=-1$, and $b = 10$ into the formula $\frac{h(b)-h(a)}{b - a}$: $\frac{h(10)-h(-1)}{10-(-1)}=\frac{39 - 17}{10 + 1}=\frac{22}{11}=2$.

Answer:

$2$