The formula for the average rate of change of a function over an interval provides a measure of how the function's value changes on average over that interval. It's often used in calculus and algebra to understand the behavior of functions. The formula is:

$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$

Here:

• $f(a)$ and $f(b)$ are the values of the function $f(x)$ at the points $a$ and $b$, respectively.
• $a$ and $b$ are the endpoints of the interval over which the rate of change is being calculated.

This formula essentially represents the slope of the secant line that passes through the points $(a, f(a))$ and $(b, f(b))$ on the graph of the function.

Would you like further examples or applications of this concept?

Here are 5 questions you might consider asking next:

1. How is the average rate of change different from the instantaneous rate of change?
2. Can you provide an example of finding the average rate of change for a specific function?
3. What does the average rate of change indicate in real-world scenarios?
4. How do you interpret the sign (positive or negative) of the average rate of change?
5. How does the average rate of change relate to the derivative of a function?

Tip: The average rate of change can help identify whether a function is increasing or decreasing over a specific interval. If the rate is positive, the function is increasing; if it's negative, the function is decreasing.