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.