the average rate of change for the line segment ab in the graph is 4 miles/hr. true false
the average rate of change for the line segment ab in the graph is 4 miles/hr. true false
Answer
Answer:
FALSE
Explanation:
Step1: Recall rate - of - change formula
The average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. For the line - segment $AB$, the distance (dependent variable) is constant from $x_1 = 2$ to $x_2 = 4$. Let $d(t)$ be the distance function with respect to time $t$. At $t = 2$, $d(2)=8$ and at $t = 4$, $d(4)=8$.
Step2: Calculate rate of change
$\frac{d(4)-d(2)}{4 - 2}=\frac{8 - 8}{2}=0$ miles/hr. So the statement that the average rate of change for the line - segment $AB$ is 4 miles/hr is false.