question given the function g(x)=x² + 9x + 14, 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, $a=-7$ and $b = - 1$.

Step2: Calculate $g(-7)$

Substitute $x=-7$ into $g(x)=x^{2}+9x + 14$. $g(-7)=(-7)^{2}+9\times(-7)+14=49-63 + 14=0$.

Step3: Calculate $g(-1)$

Substitute $x=-1$ into $g(x)=x^{2}+9x + 14$. $g(-1)=(-1)^{2}+9\times(-1)+14=1-9 + 14=6$.

Step4: Calculate the average rate of change

Use the formula $\frac{g(-1)-g(-7)}{-1-(-7)}$. $\frac{6 - 0}{-1+7}=\frac{6}{6}=1$.

Answer:

$1$