what is the average rate of change of $f(x)=x^{2}-4x - 8$ between $x=-5$ and $x = 1$?\na. 48\nb…

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