what is the average rate of change of $f(x)=x^{2}-4x - 8$ between $x=-5$ and $x = 1$?
a. 48
b. $\frac{13}{6}$
c. -8
d. 0

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here $a=-5$, $b = 1$, and $f(x)=x^{2}-4x - 8$.
## Step2: Calculate $f(-5)$
Substitute $x=-5$ into $f(x)$:
$$
\begin{align*}
f(-5)&=(-5)^{2}-4\times(-5)-8\
&=25 + 20-8\
&=37
\end{align*}
$$
## Step3: Calculate $f(1)$
Substitute $x = 1$ into $f(x)$:
$$
\begin{align*}
f(1)&=1^{2}-4\times1-8\
&=1-4 - 8\
&=-11
\end{align*}
$$
## Step4: Calculate the average rate of change
$$
\begin{align*}
\frac{f(1)-f(-5)}{1-(-5)}&=\frac{-11 - 37}{1 + 5}\
&=\frac{-48}{6}\
&=-8
\end{align*}
$$

# Answer:
C. -8

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \(f(-5)\)

Step3: Calculate \(f(1)\)

Step4: Calculate the average rate of change

Answer: