Average Rate of Change

Front

What is the 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

How do you calculate the average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where f(b) and f(a) are the function values at points b and a.

Front

What does a negative average rate of change indicate?

Back

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

Front

What does a positive average rate of change indicate?

Back

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

Front

If a car travels 60 miles in 1 hour, what is the average rate of change?

Back

The average rate of change is 60 miles per hour.

Front

What is the average rate of change from x=2 to x=5 if f(2)=10 and f(5)=25?

Back

Average Rate of Change = (25 - 10) / (5 - 2) = 15 / 3 = 5.

Front

What is the significance of the slope in a graph?

Back

The slope of a line on a graph represents the average rate of change of the function.

Front

How can you determine the interval with the greatest average rate of change from a graph?

Back

Look for the steepest slope between two points on the graph.

Front

What is the average rate of change of a climber's altitude from 400 feet to 700 feet over 4 hours?

Back

Average Rate of Change = (700 - 400) / (6 - 2) = 300 / 4 = 75 feet per hour.

Front

What is the average rate of change of a population from 1998 to 2000 if it decreased from 1000 to 800?

Back

Average Rate of Change = (800 - 1000) / (2000 - 1998) = -200 / 2 = -100 per year.