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.

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 [a, b] is the interval.

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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.

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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.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If a function's average rate of change is zero, what does that mean?

Back

It means that the function's value does not change over the interval; it is constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

Example: Find the average rate of change of f(x) = 3x + 2 from x = 1 to x = 4.

Back

Average Rate of Change = (f(4) - f(1)) / (4 - 1) = (14 - 5) / 3 = 3.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of a linear function?

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How can you interpret the average rate of change in real-life scenarios?

Back

It can represent speed, growth rate, or any change in quantity over time.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

Example: Calculate the average rate of change of height from age 3 to age 5 if height changes from 30 inches to 38 inches.

Back

Average Rate of Change = (38 - 30) / (5 - 3) = 8 / 2 = 4 inches per year.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of the function y = x^2 from x = 1 to x = 3?

Back

Average Rate of Change = (f(3) - f(1)) / (3 - 1) = (9 - 1) / 2 = 4.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6