What is the average rate of change of 
\[g\] over the interval 
\[[-1,4]\]?
Give an exact number.

To find the average rate of change of \( g \) over the interval \([-1, 4]\), we use the formula:

\[
\text{Average rate of change} = \frac{g(4) - g(-1)}{4 - (-1)}
\]

This formula calculates the slope of the line connecting the points \((-1, g(-1))\) and \((4, g(4))\) on the graph of \( g \).

1. **Evaluate \( g(4) \)** and **\( g(-1) \)** if we have expressions or values for these points.
2. Substitute the values into the formula.
3. Simplify to get the exact answer.

If you have specific values or an expression for \( g(x) \), please share them so I can provide an exact numerical answer.

Would you like more detailed steps? 

Here are 5 related questions to deepen understanding:

1. How does the average rate of change differ from the instantaneous rate of change?
2. How would the formula change if the interval were different?
3. Can the average rate of change be negative? What would that signify?
4. How does the average rate of change apply to real-world contexts?
5. What if we have a function defined piecewise over different intervals?

**Tip:** Remember that the average rate of change over an interval essentially gives the slope of the secant line through those two points.

What is the average rate of change of g over the interval [-1,4]?

Discover how to calculate the average rate of change of the function g over the interval [-1, 4]. This solution involves evaluating the function at specific points and using the average rate of change formula. Suitable for high school students.

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