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 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

What does an undefined average rate of change indicate?

Back

An undefined average rate of change indicates a vertical line, meaning there is no change in the x-values.

Front

If Pete's height increased from 40 inches to 48 inches from age 3 to 5, what is the average rate of change?

Back

4 inches per year.

Front

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

Back

Average Rate of Change = (f(4) - f(1)) / (4 - 1) = (11 - 5) / 3 = 2.

Front

What is the slope of a line that passes through points (2, 3) and (2, 7)?

Back

The slope is undefined because the x-values are the same.

Front

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

Back

Average Rate of Change = (f(3) - f(1)) / (3 - 1) = (9 - 1) / 2 = 4.

Front

If a function has a constant average rate of change, what does that imply about the function?

Back

It implies that the function is linear.