Question

the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = 0 and x = 3. use the line segment to determine the average rate of change of the function f(x) on the interval 0 ≤ x ≤ 3. plot a line segment by clicking in two locations. click a segment to delete it.

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, $a = 0$ and $b = 3$.

Step2: Find $f(0)$ and $f(3)$ from the graph

Suppose from the graph, $f(0)=y_1$ and $f(3)=y_2$.

Step3: Calculate the average rate of change

The average rate of change $=\frac{f(3)-f(0)}{3 - 0}=\frac{y_2 - y_1}{3}$.

Since the actual values of $f(0)$ and $f(3)$ are not given in text (but would be read from the graph), if we assume $f(0)= - 10$ and $f(3)= - 20$ (for illustration purposes only as we don't have actual graph - read values):
The average rate of change $=\frac{-20-( - 10)}{3}=\frac{-20 + 10}{3}=-\frac{10}{3}$.

Answer:

The average rate of change is $\frac{f(3)-f(0)}{3}$, where $f(0)$ and $f(3)$ are the $y$ - values of the function $y = f(x)$ at $x = 0$ and $x = 3$ respectively, read from the graph.