problems 27—29\nf(x)=48/x\nwrite the correct number in each box in simplest form without rounding.\n27.\nthe…

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 $\frac{f(b)-f(a)}{b - a}$.

Step2: Solve problem 27

Given $f(x)=\frac{48}{x}$, $a = 1$, $b = 24$. First, find $f(1)$ and $f(24)$. $f(1)=\frac{48}{1}=48$, $f(24)=\frac{48}{24}=2$. Then, $\frac{f(24)-f(1)}{24 - 1}=\frac{2 - 48}{23}=\frac{-46}{23}=-2$.

Step3: Solve problem 28

Given $a = 3$, $b = 12$. $f(3)=\frac{48}{3}=16$, $f(12)=\frac{48}{12}=4$. Then, $\frac{f(12)-f(3)}{12 - 3}=\frac{4 - 16}{9}=\frac{-12}{9}=-\frac{4}{3}$.

Step4: Solve problem 29

Given $a = 2$, $b = 8$. $f(2)=\frac{48}{2}=24$, $f(8)=\frac{48}{8}=6$. Then, $\frac{f(8)-f(2)}{8 - 2}=\frac{6 - 24}{6}=\frac{-18}{6}=-3$.

Answer:

27. -2
28. $-\frac{4}{3}$
29. -3