Question

average rate of change practice
complete this assessment to review what youve learned. it will not count toward your grade
use the image to answer the question
describe the behavior of the function by determining over which interval the function has a negative average rate of change. consider only intervals with consecutive endpoints shown on the graph.
(1 point)
the average rate of change is negative over the interval

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 $\frac{f(b)-f(a)}{b - a}$. If $\frac{f(b)-f(a)}{b - a}<0$, then $f(b)-f(a)$ and $b - a$ have opposite signs. Since $b>a$ (for an interval $[a,b]$), we need $f(b)

Step2: Analyze intervals on the graph

• For the interval $[0,1]$: $f(0) = 0$, $f(1)=4$, and $\frac{f(1)-f(0)}{1 - 0}=\frac{4 - 0}{1}=4>0$.
• For the interval $[1,2]$: $f(1)=4$, $f(2)=4$, and $\frac{f(2)-f(1)}{2 - 1}=\frac{4 - 4}{1}=0$.
• For the interval $[2,3]$: $f(2)=4$, $f(3)=0$, and $\frac{f(3)-f(2)}{3 - 2}=\frac{0 - 4}{1}=- 4<0$.
• For the interval $[3,4]$: $f(3)=0$, $f(4)=4$, and $\frac{f(4)-f(3)}{4 - 3}=\frac{4 - 0}{1}=4>0$.
• For the interval $[4,5]$: $f(4)=4$, $f(5)=4$, and $\frac{f(5)-f(4)}{5 - 4}=\frac{4 - 4}{1}=0$.

Answer:

$[2,3]$