To find the average rate of change of the function $f$ from $x = -6$ to $x = -5$, we can use the formula for the average rate of change:

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

where $a = -6$ and $b = -5$.

Step 1: Determine $f(-6)$ and $f(-5)$ from the graph

• From the graph, the y-value corresponding to $x = -6$ is $f(-6) = 9$.
• The y-value corresponding to $x = -5$ is $f(-5) = 4$.

Step 2: Calculate the average rate of change

$\text{Average rate of change} = \frac{f(-5) - f(-6)}{-5 - (-6)} = \frac{4 - 9}{-5 + 6} = \frac{-5}{1} = -5$

So, the average rate of change from $x = -6$ to $x = -5$ is:

$-5$

Would you like more details or have any questions?

Related Questions

1. How do you find the average rate of change for a general interval [a, b]?
2. How does the average rate of change relate to the slope of the secant line?
3. What is the physical interpretation of the average rate of change for a real-world scenario?
4. How can you determine the rate of change from a function equation instead of a graph?
5. What would the average rate of change be for different intervals on the same graph?

Tip

Always double-check the coordinates on a graph to ensure the accuracy of your calculations.