To solve the problem in the image, we need to calculate the average rate of change of the function $f(x)$ on the interval $[-8, -5]$.

The average rate of change is given by the formula:

$\text{Average rate of change} = \frac{\Delta y}{\Delta x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

Step 1: Identify the points

• From the graph, the coordinates at $x = -8$ and $x = -5$ are approximately:
  • $f(-8) \approx -25$
  • $f(-5) \approx -15$

Step 2: Calculate $\Delta y$ and $\Delta x$

• $\Delta y = f(-5) - f(-8) = -15 - (-25) = 10$
• $\Delta x = -5 - (-8) = 3$

Step 3: Find the average rate of change

$\text{Average rate of change} = \frac{10}{3} \approx 3.33$

Thus, the values you can enter are:

• $\Delta y = 10$
• $\Delta x = 3$
• Average rate of change: $3.33$

Let me know if you'd like further explanation or more details.

Here are 5 related questions you can explore:

1. How does the average rate of change relate to the slope of a line?
2. What does it mean if the average rate of change is positive or negative?
3. How do you calculate the rate of change for a non-linear function over different intervals?
4. Can the rate of change be zero for a function that isn't constant? Under what conditions?
5. How can you determine concavity or curvature using the rate of change?

Tip: The average rate of change is essentially the slope of the secant line between two points on a graph.