average rate of change quick check\nuse the image to answer the question.\ndescribe the graph of f(x) by…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. If $f(b)-f(a)<0$ and $b - a>0$ (since $b>a$ for an interval $[a,b]$), the average rate of change is negative.

Step2: Analyze interval $[1,3]$

For the interval $[1,3]$, $f(1) = 1$ and $f(3)=0$. Then $\frac{f(3)-f(1)}{3 - 1}=\frac{0 - 1}{2}=-\frac{1}{2}<0$.

Step3: Analyze interval $[6,7]$

For the interval $[6,7]$, $f(6) = 2$ and $f(7)=0$. Then $\frac{f(7)-f(6)}{7 - 6}=\frac{0 - 2}{1}=- 2<0$.

Step4: Analyze other intervals

For $[0,1]$, $f(0)=-1$ and $f(1) = 1$, $\frac{f(1)-f(0)}{1-0}=\frac{1-(-1)}{1}=2>0$. For $[3,4]$, $f(3) = 0$ and $f(4)=1$, $\frac{f(4)-f(3)}{4 - 3}=\frac{1-0}{1}=1>0$.

Answer:

The average rate of change is negative on the interval $[1,3]$ and also on the interval $[6,7]$.