https://file.aiquickdraw.com/mathbot/file/1725848318124muq212u6.jpg

The problem asks for the average rate of change of the function \( f(x) \) over the interval \([-5, 0]\). To find the average rate of change of a function over a given interval, we use the formula:

\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = -5 \) and \( b = 0 \).

### Step 1: Determine the values of \( f(-5) \) and \( f(0) \) from the graph

From the graph:

- At \( x = -5 \), the point on the graph appears to be approximately \( f(-5) = 0 \).
- At \( x = 0 \), the point on the graph is at the origin, so \( f(0) = 0 \).

### Step 2: Calculate the average rate of change

Substitute the values into the formula:

\[
\text{Average rate of change} = \frac{f(0) - f(-5)}{0 - (-5)} = \frac{0 - 0}{5} = 0
\]

### Conclusion

The average rate of change of the function \( f(x) \) on the interval \([-5, 0]\) is **0**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What does an average rate of change of 0 indicate about a function over an interval?
2. How is the average rate of change of a function related to its derivative?
3. What is the average rate of change of \( f(x) \) on a different interval, such as \([-2, 2]\)?
4. How do you find the instantaneous rate of change at a specific point on the function?
5. How would the average rate of change change if we considered a different interval, say \([-3, 1]\)?

**Tip:** Remember that the average rate of change is essentially the slope of the secant line between two points on the graph.

What is the average rate of change of the function f(x) over the interval [-5, 0]?

This problem asks to calculate the average rate of change of the function f(x) over the interval [-5, 0]. Using the formula for the average rate of change, we interpret values from the graph to solve the problem. Ideal for students in Grades 9-12.

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