Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -3 ≤ x ≤ 7?

Explanation:

Step1: Recall average rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$ and $b = 7$.

Step2: Estimate function values from graph

Suppose $f(-3)=10$ and $f(7)= - 20$ (estimated from the graph).

Step3: Calculate average rate of change

$\frac{f(7)-f(-3)}{7-(-3)}=\frac{-20 - 10}{7 + 3}=\frac{-30}{10}=-3$

Answer:

$-3$