the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…

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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$ and $b = 4$.

Step2: Find $f(-1)$ and $f(4)$ from the graph

Locate $x=-1$ and $x = 4$ on the $x$-axis and then find the corresponding $y$-values on the graph of $y = f(x)$. Suppose $f(-1)=y_1$ and $f(4)=y_2$.

Step3: Calculate the average rate of change

The average rate of change is $\frac{f(4)-f(-1)}{4-(-1)}=\frac{y_2 - y_1}{5}$.

Since the graph is not provided with specific coordinate values, we leave the answer in the general form of the average - rate - of - change formula based on the points on the graph.

Answer:

The average rate of change of $f(x)$ on the interval $-1\leq x\leq4$ is $\frac{f(4)-f(-1)}{5}$