compare the average rates of change from -1, 7. rate of change for f(x): rate of change for g(x): the rate…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a=-1$ and $b = 7$.

Step2: Find average rate of change for $f(x)$

From the graph of $f(x)$, when $x=-1$, $f(-1)=-5$ and when $x = 7$, $f(7)=5$. Then the average rate of change of $f(x)$ is $\frac{f(7)-f(-1)}{7-(-1)}=\frac{5 - (-5)}{7+1}=\frac{10}{8}=\frac{5}{4}$.

Step3: Find average rate of change for $g(x)$

From the graph of $g(x)$, when $x=-1$, $g(-1)=2$ and when $x = 7$, $g(7)=6$. Then the average rate of change of $g(x)$ is $\frac{g(7)-g(-1)}{7-(-1)}=\frac{6 - 2}{7+1}=\frac{4}{8}=\frac{1}{2}$.

Step4: Compare the two rates

Since $\frac{5}{4}>\frac{1}{2}$, the rate of change of $f(x)$ is greater than the rate of change of $g(x)$.

Answer:

rate of change for $f(x)$: $\frac{5}{4}$ rate of change for $g(x)$: $\frac{1}{2}$ The rate of change for $f(x)$ > the rate of change for $g(x)$