Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval 1 ≤ x ≤ 6?

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, $a = 1$ and $b = 6$.

Step2: Read function values from graph

From the graph, $f(1)=5$ and $f(6)= - 10$.

Step3: Calculate average rate of change

$\frac{f(6)-f(1)}{6 - 1}=\frac{-10 - 5}{5}=\frac{-15}{5}=-3$.

Answer:

$-3$