Average Rate of Change

Front

What is the definition of average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

What is the formula for calculating the average rate of change?

Back

The formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the function.

Front

How do you interpret a positive average rate of change?

Back

A positive average rate of change indicates that the function is increasing over the interval.

Front

How do you interpret a negative average rate of change?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Front

What is the average rate of change of a linear function?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.

Front

What is the average rate of change from 0 to 2 seconds if the position changes from 0 to 5 feet?

Back

The average rate of change is (5 - 0) / (2 - 0) = 2.5 feet per second.

Front

If a tank loses 10 gallons in 5 minutes, what is the average rate of change?

Back

The average rate of change is (-10 gallons) / (5 minutes) = -2 gallons per minute.

Front

What does the average rate of change tell us about a function's behavior?

Back

It provides insight into how the function's output changes with respect to its input over a specified interval.

Front

How can you find the average rate of change from a graph?

Back

By selecting two points on the graph, you can use their coordinates to apply the average rate of change formula.

Front

What is the average rate of change of the function y = 2(3)^x at the interval [2, 4]?

Back

The average rate of change is 72.