Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $2 \leq x \leq 5$?

Explanation:

Step1: Identify f(2) and f(5)

From the graph: $f(2)=4$, $f(5)=1$

Step2: Apply average rate formula

The average rate of change is $\frac{f(b)-f(a)}{b-a}$ for interval $[a,b]$.
$\text{Average rate} = \frac{f(5)-f(2)}{5-2} = \frac{1-4}{5-2}$

Step3: Calculate the value

$\frac{1-4}{5-2} = \frac{-3}{3} = -1$

Answer:

$-1$