https://file.aiquickdraw.com/mathbot/file/1727328436605phikkuf3.jpg

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.

The function y = f(x) is graphed below. Plot a line segment connecting the points on f where x = -8 and x = -5. Use the line segment to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -5.

Learn how to calculate the average rate of change of a function between two points. In this example, we use the graph of f(x) to find the rate of change on the interval [-8, -5]. Key concepts include slope, functions, and algebraic reasoning. Suitable for students in Grades 9-12.

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