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 [a, b] is the interval.

Front

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

Back

75 feet per hour.

Front

What does a negative average rate of change indicate?

Back

It indicates that the function is decreasing over the interval.

Front

What is the average rate of change of the function f(x) = 2x + 3 from x = 1 to x = 4?

Back

The average rate of change is 2.

Front

If a car travels 100 miles in 2 hours, what is its average speed?

Back

50 miles per hour.

Front

What is the average rate of change of the function f(x) = x^2 from x = 1 to x = 3?

Back

The average rate of change is 4.

Front

What is the significance of the average rate of change in real-world scenarios?

Back

It helps to understand how quantities change over time, such as speed, growth rates, and more.

Front

If a runner completes a 5K race in 25 minutes, what is their average speed in miles per hour?

Back

Approximately 7.2 miles per hour.

Front

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

Back

The average rate of change of a linear function is constant.