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ValentinaT Group Title

Can someone show me how to graph xy = 15?

  • one year ago
  • one year ago

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

    • one year ago
  2. e.mccormick Group Title
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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.

    • one year ago
  3. e.mccormick Group Title
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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.

    • one year ago
  4. ValentinaT Group Title
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    Okay.

    • one year ago
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  5. e.mccormick Group Title
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    Then play connect the dots. Remember, you can't cross either the x or y axis.

    • one year ago
  6. e.mccormick Group Title
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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.

    • one year ago
  7. e.mccormick Group Title
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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.

    • one year ago
  8. ValentinaT Group Title
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    • one year ago
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  9. e.mccormick Group Title
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    Yep! https://www.desmos.com/calculator/n7xd8g8ojy

    • one year ago
  10. ValentinaT Group Title
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    Thanks!

    • one year ago
  11. ValentinaT Group Title
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    Could you help me with one more?

    • one year ago
  12. e.mccormick Group Title
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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?

    • one year ago
  13. ValentinaT Group Title
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    Not exactly sure.

    • one year ago
  14. ValentinaT Group Title
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    Because it is undefined?

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

    • one year ago
  16. ValentinaT Group Title
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    Oh, okay.

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

    • one year ago
  18. ValentinaT Group Title
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    Alright. One more problem?

    • one year ago
  19. e.mccormick Group Title
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    Sure.

    • one year ago
  20. ValentinaT Group Title
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    Okay. \[y = \frac{ -18 }{ x }\]

    • one year ago
  21. e.mccormick Group Title
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    Same principal.

    • one year ago
  22. e.mccormick Group Title
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    It just changes what quads because of the -.

    • one year ago
  23. ValentinaT Group Title
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    • one year ago
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  24. e.mccormick Group Title
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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.

    • one year ago
  25. ValentinaT Group Title
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    Okay.

    • one year ago
  26. e.mccormick Group Title
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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.

    • one year ago
  27. ValentinaT Group Title
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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.

    • one year ago
  28. e.mccormick Group Title
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    (-1.8,10),(1.8,-10)

    • one year ago
  29. ValentinaT Group Title
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    Yeah, I just realized I did it wrong, thanks.

    • one year ago
  30. e.mccormick Group Title
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    np. Have fun!

    • one year ago
  31. ValentinaT Group Title
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    • one year ago
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  32. ValentinaT Group Title
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    Thanks for the help!

    • one year ago
  33. e.mccormick Group Title
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    Yah, not too terrible once you have the basic concept.

    • one year ago
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