How do I find the average rate of change for a function between two given values?
Average rate of change is just another way of saying "slope".
For a given function, you can take the x-values and use them to calculate the y-values, then use the slope formula:
Example: Given the function f(x) = 3x - 8, find the average rate of change between 1 and 4.
f(1) = 3(1) - 8 = -5 and f(4) = 3(4) - 8 = 4
Example: f(x) =
f(0) = 0 and f(2) = 4 - 6 = -2
Since this function is a curve, the average rate of change between any two points will be different.
You would repeat the above procedure in order to find each different slope!
If you are interested in a more advanced look at "average rate of change" for curves and non linear functions, ask about the Difference Quotient.