Average Rate of Change

Front

What is the average rate of change (ARC)?

Back

The average rate of change is a measure of how a quantity changes on average over a specific interval. It is calculated using the formula: ARC = (y2 - y1) / (x2 - x1).

Front

How do you calculate the average rate of change between two points (x1, y1) and (x2, y2)?

Back

To calculate the average rate of change, use the formula: ARC = (y2 - y1) / (x2 - x1).

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 a function has an average rate of change of 0, what does this mean?

Back

An average rate of change of 0 means that the function is constant over the interval.

Front

Calculate the average rate of change for the points (1, 2) and (5, 10).

Back

ARC = (10 - 2) / (5 - 1) = 8 / 4 = 2.

Front

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

Back

ARC = (f(3) - f(1)) / (3 - 1) = (9 - 1) / (2) = 8 / 2 = 4.

Front

How can you interpret the average rate of change in a real-world context?

Back

The average rate of change can represent speed, growth rate, or any change in quantity over time.

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

What is the significance of the points chosen for calculating average rate of change?

Back

The points chosen determine the interval over which the average rate of change is calculated, affecting the result.