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.

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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 [a, b] is the interval.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does a positive average rate of change indicate?

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A positive average rate of change indicates that the function is increasing over the interval.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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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.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

An average rate of change of 0 means that the function's value does not change over the interval.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

Example: Find the average rate of change from (2, 4) to (6, 10).

Back

Average Rate of Change = (10 - 4) / (6 - 2) = 6 / 4 = 1.5.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change in population from 1900 to 1990 if it increased from 75 million to 250 million?

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Average Rate of Change = (250 - 75) / (1990 - 1900) = 175 / 90 = 1.94 million people/year.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

It represents how much a quantity changes on average for each unit of change in another quantity.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of a climber's altitude from 400 feet to 700 feet over 4 hours?

Back

Average Rate of Change = (700 - 400) / (6 - 2) = 300 / 4 = 75 feet/hour.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6