Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-5 \leq x \leq 3$?

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 $f(-5)$ from the graph

From the graph, when $x=-5$, $f(-5)=0$

Step3: Identify $f(3)$ from the graph

From the graph, when $x=3$, $f(3)=-35$

Step4: Substitute values into the formula

$$\frac{f(3)-f(-5)}{3-(-5)} = \frac{-35 - 0}{3 + 5} = \frac{-35}{8}$$

Answer:

$\frac{-35}{8}$ or $-4.375$