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ValentinaT

  • 2 years ago

Can someone show me how to graph xy = 15?

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

  2. e.mccormick
    • 2 years ago
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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.

  3. e.mccormick
    • 2 years ago
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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.

  4. ValentinaT
    • 2 years ago
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    Okay.

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

  6. e.mccormick
    • 2 years ago
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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.

  7. e.mccormick
    • 2 years ago
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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.

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

  10. ValentinaT
    • 2 years ago
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    Thanks!

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

  12. e.mccormick
    • 2 years ago
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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?

  13. ValentinaT
    • 2 years ago
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    Not exactly sure.

  14. ValentinaT
    • 2 years ago
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    Because it is undefined?

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

  16. ValentinaT
    • 2 years ago
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    Oh, okay.

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

  18. ValentinaT
    • 2 years ago
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    Alright. One more problem?

  19. e.mccormick
    • 2 years ago
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    Sure.

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

  21. e.mccormick
    • 2 years ago
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    Same principal.

  22. e.mccormick
    • 2 years ago
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    It just changes what quads because of the -.

  23. ValentinaT
    • 2 years ago
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  24. e.mccormick
    • 2 years ago
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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.

  25. ValentinaT
    • 2 years ago
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    Okay.

  26. e.mccormick
    • 2 years ago
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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.

  27. ValentinaT
    • 2 years ago
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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.

  28. e.mccormick
    • 2 years ago
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    (-1.8,10),(1.8,-10)

  29. ValentinaT
    • 2 years ago
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    Yeah, I just realized I did it wrong, thanks.

  30. e.mccormick
    • 2 years ago
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    np. Have fun!

  31. ValentinaT
    • 2 years ago
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  32. ValentinaT
    • 2 years ago
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    Thanks for the help!

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

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