Average Rate of Change

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 is the unit of average rate of change?

Back

The unit of average rate of change depends on the context, often expressed as 'units of output per unit of input'.

Front

If a car travels 100 miles in 2 hours, what is its average rate of change?

Back

Average Rate of Change = 100 miles / 2 hours = 50 miles per hour.

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 0 to 5 if f(0) = 2 and f(5) = 12?

Back

Average Rate of Change = (12 - 2) / (5 - 0) = 10 / 5 = 2.

Front

How can you interpret the average rate of change graphically?

Back

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

Front

What is the average rate of change from 20 to 40 minutes if the function decreases from 100 gallons to 80 gallons?

Back

Average Rate of Change = (80 - 100) / (40 - 20) = -20 gallons / 20 minutes = -1 gallon per minute.

Front

What is the average rate of change between two points on a linear function?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.