Front

What is the definition of 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

What is the formula for calculating the average rate of change?

Back

The formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the function.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you interpret a positive average rate of change?

Back

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

Front

How do you interpret a negative average rate of change?

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

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

Back

The average rate of change is (5 - 0) / (2 - 0) = 2.5 feet per second.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If a tank loses 10 gallons in 5 minutes, what is the average rate of change?

Back

The average rate of change is (-10 gallons) / (5 minutes) = -2 gallons per minute.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does the average rate of change tell us about a function's behavior?

Back

It provides insight into how the function's output changes with respect to its input over a specified interval.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How can you find the average rate of change from a graph?

Back

By selecting two points on the graph, you can use their coordinates to apply the average rate of change formula.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of the function y = 2(3)^x at the interval [2, 4]?

Back

The average rate of change is 72.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6