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7.11 Variation Functions

7.11 Variation Functions. Mrs. Cassidy – it is so weird! The more I study, the worse I do!!. Babysitting, my niece earns $12 for 2 hours, $18 for 3 hours. 2 cups = 1 pint and 8 cups = 4 pints When I walked to high school at a rate of 4 miles per hour, it took me half an hour. When

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7.11 Variation Functions

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  1. 7.11 Variation Functions Mrs. Cassidy – it is so weird! The more I study, the worse I do!!

  2. Babysitting, my niece earns $12 for 2 hours, $18 for 3 hours. 2 cups = 1 pint and 8 cups = 4 pints When I walked to high school at a rate of 4 miles per hour, it took me half an hour. When I was running late and walked at a rate of 5 miles per hour, it took me 24 minutes.

  3. Variation Functions Direct Inverse

  4. Variation Functions Direct Inverse Constant  Variable Constant Variable Lets see what this looks like…

  5. Direct Variation Functions n > 0 These are called Polynomial functions What did you notice with the graph? As x went up…

  6. Inverse Variation Functions n < 0 These are called Polynomial functions What did you notice with the graph? As x goes up… The x and y axis will act as asymptotes

  7. What if no one tells you… How do you tell from a graph whether a function is a direct variation or inverse variation? How do you tell from a table of values whether a function is direct variation or inverse variation?

  8. Lets try some… Babysitting, my niece earns $12 for 2 hours, $18 for 3 hours. If x = hours and y = what she earns, what could be an equation? When kickboxing last week, I noticed that it took 5 lbs of pressure to break a board that was 2 feet long but only 1 2/3 lbs to break a board that is 6 feet long. If x = length and y = pounds of pressure, what could be an equation? y = 6x

  9. What if it isn’t quite so obvious? There are 3 steps to these types of problems 1. Determine whether it is a direct variation or inverse variation problem. 2. Look for patterns (we’ll practice this!) 3. Predict requested value

  10. Add-Add Property of Linear Functions: Given f(x) = 7x, find f(2), f(5) and f(8) For linear functions, adding a constant to x adds the constant (not necessarily the same one) to y.

  11. Add- Multiply Property of Exponential Functions Given the function f(x) = 2(3x), find f(1), f(3) and f(5) For exponential functions, adding a constant to x multiplies y by a constant.

  12. Multiply-Multiply Property of Variation Functions Given the function f(x) = 5x2, find f(1), f(2), f(4) and f(8) What does it look like you are actually multiplying each term by?

  13. Multiply-Multiply Property of Variation Functions If y = kxn, then multiplying the value of x by the constant c multiplies the value of y by the constant cn.

  14. Multiply-Multiply Property of Variation Functions If y = kxn, then multiplying the value of x by the constant c multiplies the value of y by the constant cn. If , then multiplying the value of x by the constant c divides the value of y by the constant cn.

  15. Practice Phrases y varies directly with x y varies linearly with x y varies inversely with x y is inversely proportional to x y is directly proportional to the cube of x y decreases exponentially with x y increases exponentially with x y varies inversely with the square of x y is a quadratic function of x y is a constant function

  16. Lets Practice Example 1: In a lightning storm, the time interval between the flash and bang is directly proportional to the distance between you and the lightning. A) Variables? Which should be independent? b = bang; d = distance; distance is independent B) If the thunder clap from lightening 5 km away takes 15 seconds to reach you, write the particular equation. b=5d

  17. Let’s Practice (cont) C) What is the label on the constant? s/km D) Calculate the times for the thunder sound to reach you from lightning bolts which are 1, 2.5 and 10 km away. 3, 7.5 and 30 seconds

  18. Let’s Practice more  Example 2 The intensity of radiation received for tumor treatment depends on the distance from a source. Suppose for that particular source, the intensity is 80 mr/hr at 2 meters and 5 mr/hr at 8 meters. A) What is the general equation? What is the particular equation?

  19. Let’s Practice more  Example 2 The intensity of radiation received for tumor treatment depends on the distance from a source. Suppose for that particular source, the intensity is 80 mr/hr at 2 meters and 5 mr/hr at 8 meters. A) What is the general equation? What is the particular equation?

  20. Let’s Practice more  (cont) C) What would the intensity be if your distance were 16 meters? 10 meters? 10 centimeters? D) At what distance would the intensity be 0.5 meters? 25 meters 1.25 3.2 32,000

  21. More? OF course! Truth in Advertising: In a claim in an old Time Magazine advertisement for South African Airways, one Ostrich egg is equivalent to two dozen chicken eggs.

  22. OK…. In your group, come up with the function (make up anything you want, within reason ) and find two x/y values. On another piece of paper, write the two sets of x/y values down, and then give them to another group.

  23. Resources http://mathforum.org/library/drmath/view/57504.html http://www.regentsprep.org/Regents/math/algtrig/ATE7/Inverse%20Variation.htm http://quiz.uprm.edu/tutorials/direct_var/direct_var_right.xml Your textbook

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