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 ≤ 3?

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

Step2: Estimate function values from the graph

From the graph, when $x=-3$, $f(-3)\approx - 4$ and when $x = 3$, $f(3)\approx8$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(3)-f(-3)}{3-(-3)}=\frac{8 - (-4)}{3+3}=\frac{8 + 4}{6}=\frac{12}{6}=2$.

Answer:

$2$