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 ≤ 4?

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 3$ and $b = 4$.

Step2: Estimate function values from graph

From the graph, when $x = 3$, $f(3)\approx - 10$. When $x = 4$, $f(4)\approx - 10$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(4)-f(3)}{4 - 3}=\frac{-10-(-10)}{1}=\frac{-10 + 10}{1}=0$.

Answer:

$0$