What is the average rate of change of a function

The following video provides another example of finding the average rate of change of a function given a formula and an interval. Find the average rate of change of force if the distance between the particles is increased from 2 cm to 6 cm. Skip to main content. Rates of Change and Behavior of Graphs. Search for:. A General Note: Rate of Change A rate of change describes how an output quantity changes relative to the change in the input quantity.

Example 1: Computing an Average Rate of Change Using the data in the table below, find the average rate of change of the price of gasoline between and Try It 1 Using the data in the table below, find the average rate of change between and Figure 1. Solution Figure 2. Example 3: Computing Average Rate of Change from a Table After picking up a friend who lives 10 miles away, Anna records her distance from home over time.

Solution Here, the average speed is the average rate of change. Solution We can start by computing the function values at each endpoint of the interval. Finding average rate of change from a graph. Finding average rate of change from a word problem. Linear Functions:. You are already familiar with the concept of "average rate of change". When working with straight lines linear functions you saw the "average rate of change" to be:. Non-Linear Functions:. Function f x is shown in the table at the right.

Substitute into the formula:. The average rate of change is 6 over 1, or just 6. The y -values change 6 units every time the x -values change 1 unit, on this interval.

The average rate of change of a function corresponds to the slope of the line, which connects two endpoints of a given interval known as the secant line. Here is the average rate of change formula:. The average rate of change of the function has the change in y-values in the numerator and the change in x-values as the denominator.

Since linear functions are always straight lines, their average rate of change will remain constant no matter what set of points you plug into the slope formula. Image credit: Desmos.