Average Rate of Change

Front

What is the Average Rate of Change (ARC)?

Back

The Average Rate of Change is a measure of how much a quantity changes on average over a specific interval. It is calculated as the change in the value of a function divided by the change in the input value.

Front

How do you calculate the Average Rate of Change between two points?

Back

To calculate the Average Rate of Change between two points (x1, y1) and (x2, y2), use the formula: ARC = (y2 - y1) / (x2 - x1).

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the Average Rate of Change?

Back

The Average Rate of Change is 75 feet per hour.

Front

What does it mean if the Average Rate of Change is undefined?

Back

An undefined Average Rate of Change indicates that the x-values are the same, which means the slope of the line is vertical.

Front

Which interval has the largest Average Rate of Change: [13,14], [13, 17], [16, 17], [16, 19]?

Back

The interval [16, 19] has the largest Average Rate of Change.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a function increases from 2 to 10 over the interval from 1 to 5, what is the Average Rate of Change?

Back

The Average Rate of Change is (10 - 2) / (5 - 1) = 2.

Front

What is the significance of the Average Rate of Change in real-world applications?

Back

The Average Rate of Change helps in understanding trends, such as speed, growth rates, and changes in quantities over time.

Front

How can you determine which function has the greatest rate of change?

Back

Compare the slopes of the functions over the same interval; the function with the highest slope has the greatest rate of change.