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To calculate the average rate of change of the function \( f(x) \) on the interval from \( x = 0 \) to \( x = 4 \), we will use the formula for the average rate of change:

\[
\text{Average rate of change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

In this case:
- \( x_1 = 0 \) and \( x_2 = 4 \)
- We need to find \( f(0) \) and \( f(4) \) from the graph.

From the graph:
- \( f(0) = 10 \) (the height at time \( x = 0 \))
- \( f(4) = 4 \) (the height at time \( x = 4 \))

Now we substitute these values into the formula:

\[
\text{Average rate of change} = \frac{f(4) - f(0)}{4 - 0} = \frac{4 - 10}{4} = \frac{-6}{4} = -\frac{3}{2} \, \text{feet per second}
\]

Thus, the average rate of change is \( -\frac{3}{2} \) feet per second.

Would you like further details or have any questions?

Here are 5 related questions:
1. How is the average rate of change related to the slope of a line?
2. What does the negative sign in the rate of change signify in this context?
3. How can you determine the rate of change from a table of values?
4. What happens to the rate of change when the slope of the graph is horizontal?
5. How would you calculate the rate of change over a different interval, say from \( x = 4 \) to \( x = 8 \)?

**Tip**: The rate of change in a linear graph is constant, so the slope remains the same across the entire line.

What is the average rate of change on the interval from x = 0 to x = 4?

This problem focuses on calculating the average rate of change of the linear function representing a child's elevation after sliding down from x = 0 to x = 4 seconds. The solution uses the slope formula to compute the rate of change, suitable for students in Grades 8-10.

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