for which interval is the average rate of change of f(x) negative? from x = -3 to x = 3 from x = 0 to x =…

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 $\frac{f(b)-f(a)}{b - a}$. It is negative when $f(b)-f(a)<0$ (since $b - a>0$ for a valid interval where $b>a$), i.e., $f(b)<f(a)$.

Step2: Analyze the first interval $x=-3$ to $x = 3$

From the graph, $f(-3)\approx - 3$ and $f(3)\approx - 3$, so $f(3)-f(-3)\approx0$.

Step3: Analyze the second interval $x = 0$ to $x=2.5$

From the graph, $f(0)=1$ and $f(2.5)\approx - 2$, so $f(2.5)-f(0)=-2 - 1=-3<0$.

Step4: Analyze the third interval $x = 3$ to $x=4.5$

From the graph, $f(3)\approx - 3$ and $f(4.5)\approx0$, so $f(4.5)-f(3)=0+3 = 3>0$.

Step5: Analyze the fourth interval $x=-3.5$ to $x=-1$

From the graph, $f(-3.5)\approx - 2$ and $f(-1)=1$, so $f(-1)-f(-3.5)=1 + 2=3>0$.

Answer:

from $x = 0$ to $x = 2.5$