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korosh23

  • one year ago

Calculus 12 Question! Please wait for the attachment.

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  1. korosh23
    • one year ago
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  2. korosh23
    • one year ago
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    Please explain the whole solution. I don't understand it.

  3. jim_thompson5910
    • one year ago
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    where exactly are you stuck on the solution?

  4. korosh23
    • one year ago
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    I understand the slope and that the line passes those points. However, how to get the formula and the piecewise function. I don't understand. Could you please clarify it for me?

  5. jim_thompson5910
    • one year ago
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    they broke the function into 3 linear pieces each piece is really a full linear equation, but restricted on the domain

  6. jim_thompson5910
    • one year ago
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    |dw:1443244678300:dw|

  7. jim_thompson5910
    • one year ago
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    |dw:1443244692570:dw|

  8. korosh23
    • one year ago
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    ok

  9. jim_thompson5910
    • one year ago
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    |dw:1443244719667:dw|

  10. jim_thompson5910
    • one year ago
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    |dw:1443244752626:dw|

  11. korosh23
    • one year ago
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    one question

  12. jim_thompson5910
    • one year ago
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    go ahead

  13. korosh23
    • one year ago
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    for the second lienear function f(x)= -x +2 why 2 is not the y-intercept?

  14. jim_thompson5910
    • one year ago
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    extend out the middle piece in both directions you'll see that piece cross 2 on the y axis

  15. jim_thompson5910
    • one year ago
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    |dw:1443244906871:dw|

  16. korosh23
    • one year ago
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    right :D

  17. korosh23
    • one year ago
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    one more thing, for the third function. why don't we say y=0 when x greater or equal to 2. Because at 2, y is 0

  18. jim_thompson5910
    • one year ago
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    notice the \(\Large 1 < x \le 2\) as the restriction on the second piece if x = 2, then you use y = 2-x to find y if we used \(\Large x \ge 2\) for the third piece, then that would mean x = 2 is defined for the third piece as well. Question is: which piece do we pick if x = 2? This ambiguity is a bad thing when it comes to functions. So that's why the restrictions are set up in a way to avoid letting x = 2 be defined for more than one piece

  19. jim_thompson5910
    • one year ago
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    put another way, the fancy notation you see at the bottom really breaks down into this f(x) = x if 0 <= x <= 1 OR f(x) = 2-x if 1 < x <= 2 OR f(x) = 0 if x > 2 each piece can't overlap another piece. Otherwise, we wouldn't have a function

  20. korosh23
    • one year ago
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    what do you mean by overlap?

  21. korosh23
    • one year ago
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    I believe connected does not mean overlapped

  22. jim_thompson5910
    • one year ago
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    by overlap, I mean defined in multiple places

  23. korosh23
    • one year ago
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    Oh I see, and the last question. Can we say we have 3 formulas for the function?

  24. DanJS
    • one year ago
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    Is the formal way to put the solid point on the left function, or can you do whatever for the intervals

  25. korosh23
    • one year ago
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    Ok thank you @DanJS

  26. jim_thompson5910
    • one year ago
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    think of the 3 restrictions as number lines|dw:1443245579767:dw|

  27. DanJS
    • one year ago
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    oh i didnt see tha tin the book , i was just wondering

  28. jim_thompson5910
    • one year ago
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    now if we had x >= 2 for the third piece, then we have this overlap |dw:1443245694279:dw|

  29. korosh23
    • one year ago
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    Right, hollow ones mean the number itself does not include

  30. korosh23
    • one year ago
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    So if both are full. means overlapped becaue the numbers are present in two different equations.

  31. jim_thompson5910
    • one year ago
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    exactly

  32. korosh23
    • one year ago
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    @jim_thompson5910 thank you my friend. I felt like I was in a classroom. lol

  33. DanJS
    • one year ago
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    is it legal to reverse each solid - dot combo in between functions?

  34. DanJS
    • one year ago
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    ** solid - open

  35. DanJS
    • one year ago
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    i am guessing yes, since it describes the same thing, maybe

  36. jim_thompson5910
    • one year ago
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    `is it legal to reverse each solid - dot combo in between functions?` I'm not sure what you mean. You mean use "solid" to mean "open/excluded endpoint" ? If so, then you're going against all of the conventional notation I've seen. That would be like making "up" be "down"

  37. DanJS
    • one year ago
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    I think that step function wasopen - solid

  38. DanJS
    • one year ago
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    typo corrected in next line, i just mean can you specify the intervals another way, for each interface between functions, can you choose arbitrarily which function will include the value

  39. jim_thompson5910
    • one year ago
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    oh, yeah you could say maybe 0 <= x < 1 1 <= x < 2 x >= 2 just as long as there is no overlap, you're fine

  40. DanJS
    • one year ago
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    k, that is what i was trying to say, solid-open endpoint combo switch deal.. blahh

  41. DanJS
    • one year ago
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    of course if that value is defined for both functions

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