Average Rate of Change Pre-Test

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 if f(0)=1 and f(1)=4?

Back

Average Rate of Change = (4 - 1) / (1 - 0) = 3.

Front

If the average rate of change is zero, what does it imply?

Back

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

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

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

Back

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

Front

What is the average rate of change from 20 to 40 minutes if the quantity changes from 10 to 0?

Back

Average Rate of Change = (0 - 10) / (40 - 20) = -0.5 units per minute.

Front

What is the significance of the interval in average rate of change?

Back

The interval determines the specific values of the function being compared and affects the calculated rate.