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ValentinaT

Can someone show me how to graph xy = 15?

  • 11 months ago
  • 11 months ago

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  1. e.mccormick
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    Find y, graph a few points, like the y intercept. and watch out for x=0.

    • 11 months ago
  2. e.mccormick
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    Oh, and finding the y intercept is actually a bit of a trick.... you may notice there is not one. There is also not an x intercept.

    • 11 months ago
  3. e.mccormick
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    When you solve for y, you get: \(y=\frac{15}{x}\) Any x that evenly divides 15 is a good point to use. So \(x=\{-3,-1.5,1.5,3\}\) give useful points.

    • 11 months ago
  4. ValentinaT
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    Okay.

    • 11 months ago
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  5. e.mccormick
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    Then play connect the dots. Remember, you can't cross either the x or y axis.

    • 11 months ago
  6. e.mccormick
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    (1,15), (15,1), (-1,-15), (-15,-1) are also there, so you have an idea what happens to the tails.

    • 11 months ago
  7. e.mccormick
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    The lack of an x or y intercept is one of the big clues to the shape. Do you know what that means? What quadrants your points are in is the other part of this clue.

    • 11 months ago
  8. ValentinaT
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    • 11 months ago
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  9. e.mccormick
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    Yep! https://www.desmos.com/calculator/n7xd8g8ojy

    • 11 months ago
  10. ValentinaT
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    Thanks!

    • 11 months ago
  11. ValentinaT
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    Could you help me with one more?

    • 11 months ago
  12. e.mccormick
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    Sure, but first... one concept from this type graph becomes super important later in math. Can you guess why the graph shoots up and down as it gets close to the origin?

    • 11 months ago
  13. ValentinaT
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    Not exactly sure.

    • 11 months ago
  14. ValentinaT
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    Because it is undefined?

    • 11 months ago
  15. e.mccormick
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    \(y=\frac{15}{x}\) Well, what if x is really small? Close to 0. Say \(x=\frac{1}{100}\) \[y=\frac{15}{\frac{1}{100}}\\ y=\frac{15}{1}\cdot\frac{100}{1}\\ y=1500\]

    • 11 months ago
  16. ValentinaT
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    Oh, okay.

    • 11 months ago
  17. e.mccormick
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    The undefined part then becomes what they call an asymptote. Vertical asymptotes are lines that can not be crossed.

    • 11 months ago
  18. ValentinaT
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    Alright. One more problem?

    • 11 months ago
  19. e.mccormick
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    Sure.

    • 11 months ago
  20. ValentinaT
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    Okay. \[y = \frac{ -18 }{ x }\]

    • 11 months ago
  21. e.mccormick
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    Same principal.

    • 11 months ago
  22. e.mccormick
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    It just changes what quads because of the -.

    • 11 months ago
  23. ValentinaT
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    • 11 months ago
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  24. e.mccormick
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    The important thing for easy graphing of these are factors of 18. Half points are not bad, but sometimes when you get down to weird numbers it just gets hard to graph nicely. 18 9 6 3 2 1 are all factors of 18. So they make the "easy" points this time. 1.8 is OK, just not as easy to graph as whole numbers and halfs.

    • 11 months ago
  25. ValentinaT
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    Okay.

    • 11 months ago
  26. e.mccormick
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    And you will get something like:|dw:1368216529907:dw|Not to scale this time, but I am sure that you get the point by now.

    • 11 months ago
  27. ValentinaT
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    For some reason -1.8,-10 and 1.8,10 aren't plotting right, I know you said it would be a bit harder.

    • 11 months ago
  28. e.mccormick
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    (-1.8,10),(1.8,-10)

    • 11 months ago
  29. ValentinaT
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    Yeah, I just realized I did it wrong, thanks.

    • 11 months ago
  30. e.mccormick
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    np. Have fun!

    • 11 months ago
  31. ValentinaT
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    • 11 months ago
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  32. ValentinaT
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    Thanks for the help!

    • 11 months ago
  33. e.mccormick
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    Yah, not too terrible once you have the basic concept.

    • 11 months ago
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