find the average rate of change for (f(x)=x^{2}+9x + 18) from (x=-8) to (x=-2).\na -1\nb -3\nc 1\nd 3

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-8$, $b = - 2$, and $f(x)=x^{2}+9x + 18$.

Step2: Calculate $f(-8)$

Substitute $x=-8$ into $f(x)$: [ \begin{align*} f(-8)&=(-8)^{2}+9\times(-8)+18\ &=64-72 + 18\ &=10 \end{align*} ]

Step3: Calculate $f(-2)$

Substitute $x=-2$ into $f(x)$: [ \begin{align*} f(-2)&=(-2)^{2}+9\times(-2)+18\ &=4-18 + 18\ &=4 \end{align*} ]

Step4: Calculate the average rate of change

[ \begin{align*} \frac{f(-2)-f(-8)}{-2-(-8)}&=\frac{4 - 10}{-2 + 8}\ &=\frac{-6}{6}\ &=-1 \end{align*} ]

Answer:

A. -1