Average Rate of Change

Front

What is the Average Rate of Change (ARC)?

Back

The Average Rate of Change is the change in the value of a function divided by the change in the input value over a specific interval.

Front

What is the formula for Average Rate of Change?

Back

The formula is: ARC = (y2 - y1) / (x2 - x1)

Front

If a function has values f(1) = 3 and f(5) = 15, what is the average rate of change from x=1 to x=5?

Back

The average rate of change is (15 - 3) / (5 - 1) = 12 / 4 = 3.

Front

What does a positive average rate of change indicate about a function?

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 about a function?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the average rate of change?

Back

The average rate of change is (700 - 400) / (6 - 2) = 300 / 4 = 75 feet per hour.

Front

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

Back

The average rate of change is 5 feet / 2 seconds = 2.5 feet per second.

Front

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

Back

It represents the rate at which one quantity changes in relation to another quantity over a specific interval.

Front

What is the average rate of change of a function that goes from (1, 2) to (4, 5)?

Back

The average rate of change is (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

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

Back

It implies that the function is constant over that interval.