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ValentinaT

  • one year ago

Can someone show me how to graph xy = 15?

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

  2. e.mccormick
    • one year 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
    • one year 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
    • one year ago
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    Okay.

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

  6. e.mccormick
    • one year 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
    • one year 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
    • one year ago
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  9. e.mccormick
    • one year ago
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    Yep! https://www.desmos.com/calculator/n7xd8g8ojy

  10. ValentinaT
    • one year ago
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    Thanks!

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

  12. e.mccormick
    • one year 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
    • one year ago
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    Not exactly sure.

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

  15. e.mccormick
    • one year 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
    • one year ago
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    Oh, okay.

  17. e.mccormick
    • one year 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
    • one year ago
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    Alright. One more problem?

  19. e.mccormick
    • one year ago
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    Sure.

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

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

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

  23. ValentinaT
    • one year ago
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  24. e.mccormick
    • one year 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
    • one year ago
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    Okay.

  26. e.mccormick
    • one year 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
    • one year 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
    • one year ago
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    (-1.8,10),(1.8,-10)

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

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

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

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

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