Average Rate of Change Concepts

The video tutorial explains how to find the average rate of change for the function f(x) = 1/(x+2) over the interval [3, 3+H]. It covers the steps to evaluate the function at specific points, calculate the change in output and input, and simplify the resulting expression. The tutorial emphasizes the importance of finding a common denominator and provides a formula for the average rate of change when H is greater than 0.

What is the function f(x) used in the video?

• f(x) = 1/(x+2)

• f(x) = x^2 + 2

• f(x) = 1/(x-2)

• f(x) = x + 2

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CCSS.HSF.IF.A.1

CCSS.8.F.A.1

What is the output of the function when the input is 3?

• 1/5

• 1/7

• 1/2

• 1/3

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CCSS.HSF.IF.A.2

How is the function value f(3+h) expressed?

• 1/(h+2)

• 1/(3+h)

• 1/(5+h)

• 1/(3+2h)

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

What is the change in output when calculating the average rate of change?

• 1/(5+h) - 1/5

• 1/(3+h) - 1/3

• 1/(5+h) - 1/(3+h)

• 1/(3+2) - 1/5

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

What is the change in input for the interval [3, 3+h]?

• h

• 3+h

• h+2

• 3

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CCSS.HSA.APR.D.7

What common denominator is used to simplify the expression?

• h

• 5

• 5+h

• 5 x (5+h)

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CCSS.HSA.APR.D.6

What happens to the 'h' in the expression during simplification?

• It is added

• It is subtracted

• It is simplified out

• It is multiplied

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

What is the final expression for the average rate of change?

• -1/(5 x (5+h))

• 1/(5 x (5+h))

• -h/(5 x (5+h))

• h/(5 x (5+h))

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

When can the final formula for the average rate of change be used?

• When h < 0

• For any h

• When h = 0

• When h > 0

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

What is the significance of the interval [3, 3+h] in this context?

• It is a fixed interval

• It includes a variable

• It is an open interval

• It is irrelevant

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4