Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval 5 ≤ x ≤ 7?

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, $a = 5$ and $b = 7$.

Step2: Find $f(5)$ and $f(7)$ from the graph

From the graph, when $x = 5$, $f(5)=12$; when $x = 7$, $f(7)= - 4$.

Step3: Calculate the average rate of change

Substitute $f(5)=12$, $f(7)= - 4$, $a = 5$, and $b = 7$ into the formula: $\frac{f(7)-f(5)}{7 - 5}=\frac{-4 - 12}{2}=\frac{-16}{2}=-8$.

Answer:

$-8$