12/09 & 12/10 HW: 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 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

If a family traveled 204 miles in 3 hours, what was their Average Rate of Change in miles per hour?

Back

Average Rate of Change = 204 miles / 3 hours = 68 mph.

Front

What is the significance of the slope in a graph?

Back

The slope represents the Average Rate of Change of the function represented by the graph.

Front

How can you interpret the Average Rate of Change in real-life scenarios?

Back

It can represent speed, growth rate, or any change over time, such as distance traveled or population growth.

Front

What is the Average Rate of Change between the points (2, 5) and (4, 9)?

Back

Average Rate of Change = (9 - 5) / (4 - 2) = 4 / 2 = 2.

Front

What is the Average Rate of Change of a quadratic function?

Back

The Average Rate of Change of a quadratic function varies depending on the interval chosen.