Average Rate of Change NYS Regents Practice

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 f(b) and f(a) are the function values at points b and a.

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 a positive average rate of change indicate?

Back

A positive average rate of change indicates that the function is increasing over the interval.

Front

If a bird glides from 100 feet to 50 feet over 10 seconds, what is the average rate of change?

Back

Average Rate of Change = (50 - 100) / (10 - 0) = -5 feet per second.

Front

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

Back

It helps to understand how quantities change over time, such as speed, growth rates, and other dynamic processes.

Front

What is the average rate of change between the points (1, 2) and (4, 5)?

Back

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

Front

What is the average rate of change if a function is constant?

Back

If a function is constant, the average rate of change is 0, indicating no change in value.

Front

How can you interpret the average rate of change graphically?

Back

Graphically, the average rate of change corresponds to the slope of the secant line connecting two points on the graph of the function.

Front

What is the average rate of change of a function at a specific point?

Back

The average rate of change at a specific point can be approximated using the derivative, which gives the instantaneous rate of change.