Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-5 \leq x \leq -4$?

Explanation:

Step1: Identify $f(-5)$ and $f(-4)$

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

Step2: Apply average rate formula

The average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=-5$, $b=-4$:
$\frac{f(-4)-f(-5)}{-4-(-5)} = \frac{-2-2}{-4+5}$

Step3: Calculate the result

$\frac{-4}{1} = -4$

Answer:

$-4$