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9.1 Inverse Variation

9.1 Inverse Variation. A direct variation is a linear function of the form y = kx. A function of the form y = k/x is called an inverse variation . k is the nonzero constant of variation. Example:

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9.1 Inverse Variation

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  1. 9.1 Inverse Variation

  2. A direct variation is a linear function of the form y = kx. A function of the form y = k/x is called an inverse variation. k is the nonzero constant of variation.

  3. Example: Suppose that x and y vary inversely, and x=3 when y=-5. Write the function that models the inverse variation. y = k/x -5 = k/3 k = -15 so y = -15/x

  4. Combined variation: combines direct and inverse variations in more complicated relationships. Examples: y varies directly with the square of x y = kx2 z varies jointly with x and y z = kxy z varies directly with x and inversely with the product of w and y. z = kx/(wy)

  5. Write a model if z varies directly with x and inversely with y. When x=6, y=2, z=15. Find z when x=4 and y=9 Answer: z= 5x/y z = 20/9

  6. Hw pg 481 1-27 all

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