Question

the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = 1 and x = 8. use the line segment to determine the average rate of change of the function f(x) on the interval 1 < x < 8.

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, $a = 1$ and $b=8$.

Step2: Identify values from the graph

We need to find $f(1)$ and $f(8)$ from the graph of the function $y = f(x)$. Let's assume that from the graph, $f(1)=y_1$ and $f(8)=y_2$.

Step3: Calculate average rate of change

The average rate of change $=\frac{f(8)-f(1)}{8 - 1}=\frac{y_2 - y_1}{7}$.

Answer:

The average rate of change of the function $f(x)$ on the interval $1