Final answer:
The average rate of change of a function is calculated as the slope of the line connecting two points on the function's graph, which correspond to the interval's endpoints. It is the change in function values divided by the change in the interval values.
Step-by-step explanation:
To find the average rate of change of a function over a given interval, you essentially calculate the slope of the straight line that connects two points on the graph of the function. The points correspond to the end values of the interval you're considering. The formula to calculate the average rate of change is:
\( \frac{f(b) - f(a)}{b - a} \)
where a and b are the endpoints of the interval, and f(a) and f(b) are the values of the function at these points.
For example, if you want to calculate the average rate of change of a function f(x) from x = 1 to x = 4, and the function values at those points are f(1) = 2 and f(4) = 10, then:
\( \frac{f(4) - f(1)}{4 - 1} = \frac{10 - 2}{3} = \frac{8}{3} \)
This result is the average rate of change over the interval from x = 1 to x = 4.
The complete question is: Determine the Average Rate of Change of a Function Over a Given Interval.