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Variation Functions

Variation Functions. Variation functions are equations in which y is equal to a constant multiplied or divided by a power of x. If the constant is multiplied by the variable, then y varies directly with the power of x.

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Variation Functions

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  1. Variation Functions Variation functions are equations in which y is equal to a constant multiplied or divided by a power of x. If the constant is multiplied by the variable, then y varies directly with the power of x. If the constant is divided by the variable, then y varies inversely with the power of x.

  2. Variation Functions If k and n are constants, then “y varies directly with the power of x” means: and “y varies inversely with the power of x means:

  3. Variation Functions The constant is called the proportionality constant. The letter k is often used as the constant.

  4. y varies directly with x: • yvaries directly with the square of x: • yvaries directly with the cube of x: • y varies indirectly with x: • y varies indirectly with the square of x:

  5. Variation Functions Direct Variation:y gets bigger as x increases Inverse Variation: y gets smaller as x increases • x- and y-axes are the asymptotes

  6. Variation Functions To solve a variation problem: 1) Look at the ordered pairs given to you in the problem. Figure out how x and y are changing in relation to each other. 2) Write the general rule you will use. 3) Set your variables. 4) Write the particular equation. 5) Use the particular equation to make predictions.

  7. Example 1 (Page 387) • The pressure required to force water through a garden hose depends on the number of gallons per minute (gpm) you want to flow. By experiment, you find that for a flow of 3 gpm, a pressure of 10 pounds per square inch (psi) is required. For 6 gpm, a pressure of 40 psi is required. • Predict the following: • the pressure required for a flow rate of 12 gpm. • the pressure required for a flow rate of 4.2 gpm • the number of gpm you would get with a pressure of 5 psi.

  8. Example 2 (page 389) • The intensity of light reaching you from a light bulb depends on how far from the bulb you are standing. Suppose that at 3 meters the intensity is 120 units, and at 6 meters it is 30 units. • How does the intensity vary with distance? Write the general equation. • Find the particular equation. • Predict the intensity at 10 meters • Predict the intensity at 12 meters • Predict the distance at which the intensity with be 4 units.

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