Average Rate of Change NYS Regents 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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you calculate the average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where f(b) and f(a) are the function values at points b and a.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change in profit if the profit increases from $100 to $300 over 10 hours?

Back

Average Rate of Change = (300 - 100) / (10 - 0) = 20 dollars per hour.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If a family travels 204 miles in 3 hours, what is their average rate of change in miles per hour?

Back

Average Rate of Change = 204 miles / 3 hours = 68 miles per hour.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the significance of the average rate of change in real-life scenarios?

Back

It helps in understanding how quantities change over time, such as speed, profit, or population growth.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change if a car travels 150 miles in 2 hours?

Back

Average Rate of Change = 150 miles / 2 hours = 75 miles per hour.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If the temperature changes from 30°F to 50°F over 4 hours, what is the average rate of change in temperature?

Back

Average Rate of Change = (50 - 30) / (4 - 0) = 5°F per hour.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change in a function's value if it goes from 10 to 50 over an interval of 5 units?

Back

Average Rate of Change = (50 - 10) / (5 - 0) = 8 units per unit.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6