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Find average rate of change of the function on the interval [-3,2]

To find the average rate of change of the function on the interval \([-3, 2]\), we use the formula for the average rate of change between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
\text{Average Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the graph:
- At \(x_1 = -3\), the function value \(y_1 = -2\).
- At \(x_2 = 2\), the function value \(y_2 = 4\).

Plugging these values into the formula:

\[
\text{Average Rate of Change} = \frac{4 - (-2)}{2 - (-3)} = \frac{4 + 2}{2 + 3} = \frac{6}{5} = 1.2
\]

So, the average rate of change of the function on the interval \([-3, 2]\) is \(1.2\).

Would you like more details or have any other questions? 

Here are 5 related questions that might help you understand this topic better:
1. How does the average rate of change relate to the slope of a line in a linear function?
2. What does it mean when the average rate of change is positive or negative?
3. How can you interpret the average rate of change for different types of functions?
4. What is the difference between instantaneous rate of change and average rate of change?
5. How do you find the average rate of change for a function over a given interval using calculus?

**Tip:** The average rate of change gives you an idea of how the function behaves on average between two points, and it can be visualized as the slope of the secant line connecting those points on the graph.

Find the average rate of change of the function on the interval [-3, 2].

Learn how to find the average rate of change of a function between two points on the interval [-3, 2] using the formula for the slope of the secant line. This problem involves calculating the difference in function values over the interval and is suitable for students in Grades 9-12.

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