Average Rate of Change

Definition and Calculation

The average rate of change of a function f(x) between two points x_1 and x_2 measures how much the function's output changes per unit change in input over that interval. It is calculated using the formula:

• f(x): The function being analyzed.

• x_1, x_2: The endpoints of the interval.

Example: Linear Function

Given the function:

and the interval:

First, compute the function values:

Now, apply the formula:

Rounded to two decimal places: 3.00

Graphical Interpretation

• The average rate of change over an interval on a linear function is equal to the slope of the line.

• For , the slope is 3, which matches the calculated average rate of change.

• On a graph, this means that for every unit increase in , increases by 3 units.

Key Points

• Linear functions have a constant average rate of change over any interval.

• The average rate of change is visually represented by the steepness of the graph (the slope).

Summary Table