Inverse Variation and Function Relationships

This video tutorial introduces the concept of inverse variation, providing a definition and solving related problems. It begins with real-life examples, such as travel time and speed, and the cost of gasoline per person. The video explains the formal definition and equations of inverse variation, including the constant of proportionality. Several examples are solved, including emptying a tank, breaking a board, and a variation involving the square root. The tutorial emphasizes understanding the relationship between variables in inverse variation and how to apply it to solve problems.

Which of the following is an example of inverse variation?

• The more you work, the more money you earn.

• The more you eat, the more weight you gain.

• The faster you drive, the less time it takes to reach your destination.

• The more you study, the higher your grades.

What is the equation that represents inverse variation?

• Y = X / K

• Y = K * X

• Y = K + X

• Y = K / X

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CCSS.HSF-IF.C.7E

In the graph of Y = K/X, what happens to Y as X increases?

• Y becomes zero

• Y remains constant

• Y decreases

• Y increases

If Y = 8/X and X = 16, what is the value of Y?

• 4

• 2

• 1/2

• 1

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CCSS.HSF-LE.A.1B

In the tank emptying example, what happens to the time required as the rate of pumping increases?

• Time increases

• Time decreases

• Time remains the same

• Time doubles

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CCSS.HSA.CED.A.1

If a pump empties a tank in 2.5 hours at 400 gallons per minute, how long will it take at 500 gallons per minute?

• 2 hours

• 3 hours

• 1.5 hours

• 2.5 hours

In the board breaking example, what is the relationship between force and length?

• Inverse variation

• Exponential variation

• Direct variation

• No variation

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CCSS.6.EE.B.7

If it takes 24 pounds of pressure to break a 2-foot board, how much pressure is needed for a 5-foot board?

• 15 pounds

• 9.6 pounds

• 20 pounds

• 12 pounds

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CCSS.8.EE.A.2

In the variation involving the square root of X, what is the equation used?

• Y = K * sqrt(X)

• Y = X / sqrt(K)

• Y = K / sqrt(X)

• Y = sqrt(K) / X

If Y = 24/sqrt(X) and X = 4, what is the value of Y?

• 10

• 8

• 12

• 6