given the function g(x)=x² - 10x + 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, $a = 1$, $b = 11$, and $g(x)=x^{2}-10x + 18$.

Step2: Calculate $g(1)$

Substitute $x = 1$ into $g(x)$: $g(1)=1^{2}-10\times1 + 18=1-10 + 18=9$.

Step3: Calculate $g(11)$

Substitute $x = 11$ into $g(x)$: $g(11)=11^{2}-10\times11 + 18=121-110 + 18=29$.

Step4: Calculate the average rate of change

Use the formula $\frac{g(11)-g(1)}{11 - 1}$. $\frac{g(11)-g(1)}{11 - 1}=\frac{29 - 9}{10}=\frac{20}{10}=2$.

Answer:

$2$