Rate of Change
Rate of change is the just the slope of the line that would run between two points. Sometimes, we're asked to find the average rate of change for a curved function (ex: quadratic or exponential functions).
No matter what kind of function we're looking at, the process is the same. We're going to pick two points and find the slope of the line that has both of those points on it. To do that, we're going to |
figure the change in y values over (or divided by) the change in x vales. When we're dealing with a nonlinear function, the rate of change varies depending on which section of the function we're looking at. (Think about a parabola. It's decreasing steeply for a while, the decreasing shallowly, then increasing by varying amounts.)
If you've also been asked to graph the equation, the easiest way to find the average rate of change is to count the rise over run between the two points.
Sometimes, we're asked to find the average rate of change for -1<x<1. What this means is that we need to use the points where x=-1 and the where x=1. To do this, you can plug the two values in for x and solve the equations for y. Now you have two points to use in your slope equation even you don't know where to start with graphing the equation. (See last video at the bottom of this page.)
If you've also been asked to graph the equation, the easiest way to find the average rate of change is to count the rise over run between the two points.
Sometimes, we're asked to find the average rate of change for -1<x<1. What this means is that we need to use the points where x=-1 and the where x=1. To do this, you can plug the two values in for x and solve the equations for y. Now you have two points to use in your slope equation even you don't know where to start with graphing the equation. (See last video at the bottom of this page.)
Videos by Sal Kahn
Slope and Rate of Change (of linear functions)
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Average Rate of Change: Example 1
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Average Rate of Change: Example 2
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Average Rate of Change: Example 3
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Average Rate of Change when Defined by an Equation
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