AROC 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

To calculate the average rate of change, use the formula: (f(b) - f(a)) / (b - a), where f(b) and f(a) are the function values at points b and a.

Front

What is the average rate of change from 0 to 2 seconds if the distance is 5 feet?

Back

2.5 feet per second.

Front

If a climber's altitude changes from 400 feet to 700 feet over 4 hours, what is the average rate of change?

Back

75 feet per hour.

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 the function f(x) = 2x + 1 from x=0 to x=1?

Back

3.

Front

If the average rate of change is 0, what does it imply about the function?

Back

It implies that the function is constant over that interval.

Front

What is the average rate of change from 20 to 40 minutes if the gallons used are 40 and 20 respectively?

Back

-2 gallons per minute.

Front

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

Back

It helps to understand how one quantity changes in relation to another, such as speed, growth rates, and efficiency.

Front

How can you interpret the average rate of change graphically?

Back

Graphically, the average rate of change is represented by the slope of the secant line connecting two points on the graph of the function.