A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Anikate

  • one year ago

find hole, HA, SA, VA, x-int, and y-int. Posting question. please help.

  • This Question is Closed
  1. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1434344992559:dw|

  2. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    omg my brain hurts... factor out the x's in the equation then x-intercept occurs when y = 0 y-intercept occurs when x = 0

  3. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how do u know those x and y ints?

  4. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what I wrote is the definition... hmm I think you have to set y = 0 for x-intercept and set x = 0 for y-intercept.. x.x I'm tired

  5. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh lol sorry didnt notice, im just as fried XD 1:13AM here

  6. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, after factorign out x's, what now?

  7. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    brain hurts x.x

  8. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i feel ya. u live in USA?

  9. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

  10. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    east coast?

  11. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you must live in the east coast. I'm 6 hours behind you

  12. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

  13. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it's only 7:16 pm in my state

  14. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    mann lucky you!

  15. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so how do u find hole, VA, HA, SA?

  16. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I am ... tired...so sorry @ganeshie8 take over xD

  17. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    kk np

  18. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434345612001:dw|

  19. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    set the denominator equal to \(0\) to get VA/holes

  20. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  21. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    SA?

  22. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    First find VA/holes, show ur work so that i know u got it

  23. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh ok

  24. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1434345921379:dw|

  25. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8

  26. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    why are you plugging in 0 in place of x ? |dw:1434346170455:dw|

  27. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    For VA/holes you simply need to set the denominator equal to 0 and solve x |dw:1434346189911:dw|

  28. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ooh waitI got it, sorry my brain is half dea. ill do the work again

  29. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1434346226956:dw|

  30. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes, so x=0 and x=4 are discontinuities you need to figure out which of them are holes and VAs

  31. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how do i do that?

  32. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    do you know how to tell whether a discontinuity is a hole or a VA ?

  33. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no....

  34. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Okay, it is easy. look at the given rational expression |dw:1434346474036:dw|

  35. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The factor \(\large x\) is common to both numerator and denominator. Therefore \(x=0\) is a hole

  36. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the factor \((x-4)\) is not there in the numerator, so \(x=4\) is a VA

  37. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont understand how u got x=4 because it is not in the numerator? what does the denominator have to do with the numerator?

  38. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    do you see \(x\) is there in both numerator and denominator but \(x-4\) is there only in the denominator ?

  39. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  40. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Since the factor \(x\) cancels out, \(x=0\) is a hole.

  41. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  42. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Since the factor \(x-4\) does not cancel out, so \(x-4=0\) is a VA.

  43. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Notice that \(x-4=0\) is same as \(x=4\)

  44. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh ok

  45. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    basically you need to see what factors are common to both numerator and denominator for holes

  46. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so VA is just the denominator after the entire equation is simplified?

  47. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes

  48. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, and how about SA?

  49. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so what do we have so far

  50. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hole: x=0 VA: X=4 SA: ?

  51. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

  52. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    how do you know there exists a SA ?

  53. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no clue :(

  54. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    do you know how to tell the degree of a polynomial ?

  55. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the degree of the first exponent

  56. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes, look at the given rational expression again. Degree of numerator = ? Degree of denominator = ?

  57. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    numerator: 3 denominator: 2

  58. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes! degree of numerator is just 1 greater than the degree of denominator so there exists a SA

  59. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    knw how to find the SA ?

  60. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    simply do long division

  61. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    remember long division ?

  62. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    vaguely

  63. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how do i do it for this?

  64. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434348039440:dw|

  65. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434348112918:dw|

  66. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how do subtract the x and 12 x^2?

  67. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Oh yes, we cant subtract apples and coconuts, so we just leave it as it is : |dw:1434348286262:dw|

  68. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434348365527:dw|

  69. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    we're done because when you subtract you will get a remainder whose degree is less than the denominator., so the SA is \[\large y=3x+12\]

  70. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh cool! hot it! thanks!!

  71. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    got it*

  72. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    good, notice that there wont be any HA because the degree of numerator is high

  73. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    what about x-int and y-int ?

  74. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok and the x-in, y-int is y-int: 0 x-int: 0

  75. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8 is that right?

  76. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    doesn't look correct

  77. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \(x=0\) is a hole, so there are no y intercepts.

  78. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for x intercepts, you set y = 0|dw:1434349076055:dw|

  79. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434349091942:dw|

  80. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434349134532:dw|

  81. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434349181041:dw|

  82. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so there could be infinite answers?

  83. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434349240955:dw|

  84. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434349306136:dw|

  85. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the solutions when setting the numerator to 0 are : \(\large x = 0,~\frac{1}{\sqrt{3}},~-\frac{1}{\sqrt{3}}\)

  86. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    But \(x=0\) is a hole, so discard that.

  87. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The x intercepts are : \(\large \frac{1}{\sqrt{3}},~~-\frac{1}{\sqrt{3}}\)

  88. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    see if that makes more or less sense

  89. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry, slow internet. so the x-intercepts matters on the numerator??

  90. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ganeshie8

  91. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Notice, x intercepts are points on x axis so the y value will be 0

  92. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    setting y = 0, makes the denominator vanish

  93. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so yes, in that sense only the numerator matters for x intercepts

  94. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how? can we just set x to 0 and get y=0 as an answer?

  95. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    tell me this, what exactly is an x intercept ?

  96. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where the y=0

  97. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    explain more

  98. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where the line on the graphs crosses the x-axis

  99. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Exactly! when the curve intersects the x axis, the y value will be 0, yes ?

  100. Anikate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

  101. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434350344473:dw|

  102. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1434350374270:dw|