Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-4 \leq x \leq -3$?

Explanation:

Step1: Identify $f(-4)$ and $f(-3)$

From the graph: $f(-4)=0$, $f(-3)=-4$

Step2: Apply average rate formula

The formula for average rate of change on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=-4$, $b=-3$:
$\frac{f(-3)-f(-4)}{-3-(-4)} = \frac{-4 - 0}{-3 + 4}$

Step3: Calculate the result

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

Answer:

$-4$