To find the average rate of change of $y$ over the interval $[-2, 0]$, we can use the formula for the average rate of change between two points $(x_1, y_1)$ and $(x_2, y_2)$:

$\frac{y_2 - y_1}{x_2 - x_1}$

In this case:

• For $x = -2$, $y = 27$.
• For $x = 0$, $y = 11$.

So, plugging these values into the formula:

$\frac{11 - 27}{0 - (-2)} = \frac{-16}{2} = -8$

Thus, the average rate of change over the interval $[-2, 0]$ is:

Answer: B. $-8$

Would you like more details or have any questions?

Here are five related questions that expand on this topic:

1. How would the average rate of change change if we used a different interval, like $[-1, 1]$?
2. What does a negative average rate of change indicate about the relationship between $x$ and $y$ in this interval?
3. How can we interpret the average rate of change geometrically on a graph?
4. How would you compute the average rate of change if the interval had more complex values, like $[-2.5, 0.5]$?
5. Can you find the point in the table where the rate of change between consecutive values is zero?

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