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: Recall average rate of change formula

The average rate of change of $f(x)$ on $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify $a, b, f(a), f(b)$

For interval $-4 \leq x \leq -3$, $a=-4$, $b=-3$. From the graph: $f(-4)=4$, $f(-3)=-4$.

Step3: Substitute values into formula

$\frac{f(-3)-f(-4)}{-3-(-4)} = \frac{-4 - 4}{-3 + 4}$

Step4: Calculate the result

$\frac{-8}{1} = -8$

Answer:

$-8$