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Destinyyyy

  • one year ago

Whats the trick for knowing which ( ) or [ ] go where in interval notation?

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  1. Destinyyyy
    • one year ago
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    Like... (- infinity sign, infinity sign) (- infinity sign, -1] (-3,0] [-1,8)

  2. BishopPatton
    • one year ago
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    Let's draw a number line with these four special numbers marked: -x <------o----o----o----o----0----o----o----o----o------> +x -3 -1 1 3 The trick is to look at the sign (+ or -) of your expression in each one of the intervals where nothing changes sign from + to - or back. These intervals are "up to but not including -3", "strictly between -3 and -1", etc. There are 5 of them. As an example, let's see what happens between -1 and +1. The numerator has one positive factor and one negative factor. The same is true for the denominator. So both numerator and denominator are negative, making the fraction > 0. Now we know that it is >= 0 in the interval (-1,+1). Remember the fraction is 0 for x=-1 and undefined for +1, so we write [-1,+1); the square cornered bracket on the left shows -1 IS IN the interval we are talking about where the fraction is >= zero. With me so far? Now do this kind of analysis about the 4 other sub-intervals to see what happens. As for the graph for such a problem, just draw on the number line to show what x values are included. There are two ways to show that an end point is or isn't included in the graph. Some books use "[" and "(" for this and some use a filled-dot and hollow-dot for it. Look in your book. I hope this helps.

  3. BishopPatton
    • one year ago
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    i am tired as heck after having to type that lol

  4. BishopPatton
    • one year ago
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    Please medal and fan if this helps you

  5. welshfella
    • one year ago
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    note when one of the numbers infinity or - infinity it's always a '(' or ')'

  6. BishopPatton
    • one year ago
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    Yep

  7. Destinyyyy
    • one year ago
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    Um what?

  8. Destinyyyy
    • one year ago
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    I have no clue what dot things your talking about. I dont have a book to look at

  9. BishopPatton
    • one year ago
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    if you read everything outloud to yourself it will make sense

  10. Destinyyyy
    • one year ago
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    My examples show ( ) and [ ]

  11. BishopPatton
    • one year ago
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    That is all i can do to help. i hope you understand

  12. Destinyyyy
    • one year ago
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    I rather no draw a number line for every problem I do.. Is there a easier way

  13. Destinyyyy
    • one year ago
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    not *

  14. Destinyyyy
    • one year ago
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    It doesnt matter if I read it allowed or not I dont understand anything you said.

  15. welshfella
    • one year ago
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    one of your examples is (-3,0] that means 'greater than -3 and less than and including 0'.

  16. Destinyyyy
    • one year ago
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    Okay I get that.. And my examples were just to show someone what Im talking about

  17. welshfella
    • one year ago
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    so are you happy with the answers given?

  18. Destinyyyy
    • one year ago
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    Um not really.. Im still where I was before.. Can you maybe give me an example to solve or something? Im working with domain and range right now

  19. welshfella
    • one year ago
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    ok so what does [ , INf sign) mean

  20. Destinyyyy
    • one year ago
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    ? Like [1, infinity sign) ??

  21. welshfella
    • one year ago
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    yes

  22. Destinyyyy
    • one year ago
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    Okay.. [ means less than and including 1.. ) means greater than infinity

  23. welshfella
    • one year ago
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    No It means greater than and including 1 and up to infinity

  24. Destinyyyy
    • one year ago
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    I dont get it then

  25. welshfella
    • one year ago
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    - in other words all numbers from and including 1 and going on infinaiely

  26. welshfella
    • one year ago
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    well try an easy one {3 , 6) this is all numbers greater than and including 3 and less than 6 the [ means that 3 is included and the ) at the end means 6 is NOT included

  27. welshfella
    • one year ago
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    that the square bracket [

  28. welshfella
    • one year ago
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    means 'included'

  29. Destinyyyy
    • one year ago
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  30. welshfella
    • one year ago
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    also its important to remember that its a continuum of numbers between these to values not just 4 and 5 its 3.9011, 5.5 , 5.9999 and whatever

  31. Destinyyyy
    • one year ago
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    This is what im working on. I really understand what you just said. Im trying to but its not making any sense to me

  32. Destinyyyy
    • one year ago
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    I dont care about that. I just want to know how to know where to put () and []

  33. Destinyyyy
    • one year ago
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    I assumed there was some trick people knew that helped them figure it out quick.

  34. triciaal
    • one year ago
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    when you have square it includes the end values

  35. welshfella
    • one year ago
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    the domain is all the values of x that the function can take the empty circle means that that values of x is not included and the filled means that values of x is included.

  36. Destinyyyy
    • one year ago
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    Yes..

  37. welshfella
    • one year ago
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    yes the domain for that function is (-3,0]

  38. welshfella
    • one year ago
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    the x -3 has the emplty circle but x = 0 has filled one

  39. Destinyyyy
    • one year ago
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    Yeah.. But how do you know where to put the 9 and ] at??

  40. Destinyyyy
    • one year ago
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    ( ] **

  41. welshfella
    • one year ago
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    well ( when the number is not included - so it comes before the -3

  42. welshfella
    • one year ago
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    |dw:1441818059986:dw|

  43. Destinyyyy
    • one year ago
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    Um okay I think I understand that..

  44. Destinyyyy
    • one year ago
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    So the range would be (5,-4] ??

  45. welshfella
    • one year ago
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    the lowest value of y comes first in the range this is -5 and the highest is 5

  46. welshfella
    • one year ago
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    Sorry lowest is -4

  47. Destinyyyy
    • one year ago
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    So [-4,5)

  48. welshfella
    • one year ago
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    yes

  49. welshfella
    • one year ago
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    -4 is included but 5 is not

  50. Destinyyyy
    • one year ago
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    Okay I think I understand

  51. welshfella
    • one year ago
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    good

  52. Destinyyyy
    • one year ago
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    Thank you.

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