Average Rate of Change Problems

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 from x=0 to x=1 for the function f(x) = 3x?

Back

3.

Front

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

Back

It means that the function's value does not change over the interval.

Front

What is the average rate of change from x=2 to x=6 for the function f(x) = 100 - 5x?

Back

-20.

Front

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

Back

It can represent speed, growth rate, or any change in quantity over time.

Front

What is the average rate of change for a linear function?

Back

For a linear function, the average rate of change is constant.

Front

What is the average rate of change from 0 to 2 seconds if Mrs. Gordon travels 5 feet?

Back

2.5 feet per second.