Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval 4 ≤ x ≤ 6?

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, $a = 4$ and $b = 6$.

Step2: Determine $f(4)$ and $f(6)$ from the graph

From the graph, when $x = 4$, $f(4)=8$; when $x = 6$, $f(6)= - 12$.

Step3: Calculate the average rate of change

Substitute $f(4)=8$, $f(6)= - 12$, $a = 4$, and $b = 6$ into the formula: $\frac{f(6)-f(4)}{6 - 4}=\frac{-12 - 8}{2}=\frac{-20}{2}=-10$.

Answer:

$-10$