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

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x is zero.

Front

What is the average rate of change of a function on the interval [1, 5] if f(1) = 2 and f(5) = 5?

Back

Average Rate of Change = (5 - 2) / (5 - 1) = 3/4.

Front

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

Back

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

Front

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

Back

It helps to understand how a quantity changes over time, such as speed, growth, or decline.

Front

What is the average rate of change of Pete's height from 3 years old to 5 years old if he grows from 36 inches to 44 inches?

Back

Average Rate of Change = (44 - 36) / (5 - 3) = 4 inches per year.

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

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

If the average rate of change is zero, what does that mean?

Back

It means the function's value does not change over the interval.