Question

the function y = f(x) is graphed below. what is the average rate of change of f(x) on the interval 4 ≤ x ≤ 6?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$ and $b = 6$.

Step2: Estimate $f(4)$ and $f(6)$ from the graph

Suppose from the graph, $f(4)=y_1$ and $f(6)=y_2$.

Step3: Calculate the average rate of change

The average rate of change is $\frac{f(6)-f(4)}{6 - 4}=\frac{y_2 - y_1}{2}$.

Answer:

The average rate of change is $\frac{f(6)-f(4)}{2}$, where $f(4)$ and $f(6)$ are the $y$ - values of the function $y = f(x)$ at $x = 4$ and $x = 6$ respectively, estimated from the graph.