## Anikate one year ago find hole, HA, SA, VA, x-int, and y-int. Posting question. please help.

1. Anikate

|dw:1434344992559:dw|

2. UsukiDoll

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

how do u know those x and y ints?

4. UsukiDoll

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

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

6. Anikate

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

7. UsukiDoll

brain hurts x.x

8. Anikate

i feel ya. u live in USA?

9. UsukiDoll

yup

10. Anikate

east coast?

11. UsukiDoll

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

12. Anikate

yup

13. UsukiDoll

it's only 7:16 pm in my state

14. Anikate

mann lucky you!

15. Anikate

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

16. UsukiDoll

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

17. Anikate

kk np

18. ganeshie8

|dw:1434345612001:dw|

19. ganeshie8

set the denominator equal to $$0$$ to get VA/holes

20. Anikate

ok

21. Anikate

SA?

22. ganeshie8

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

23. Anikate

oh ok

24. Anikate

|dw:1434345921379:dw|

25. Anikate

@ganeshie8

26. ganeshie8

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

27. ganeshie8

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

28. Anikate

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

29. Anikate

|dw:1434346226956:dw|

30. ganeshie8

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

31. Anikate

how do i do that?

32. ganeshie8

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

33. Anikate

no....

34. ganeshie8

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

35. ganeshie8

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

36. ganeshie8

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

37. Anikate

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

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

39. Anikate

yes

40. ganeshie8

Since the factor $$x$$ cancels out, $$x=0$$ is a hole.

41. Anikate

ok

42. ganeshie8

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

43. ganeshie8

Notice that $$x-4=0$$ is same as $$x=4$$

44. Anikate

oh ok

45. ganeshie8

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

46. Anikate

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

47. ganeshie8

Yes

48. Anikate

49. ganeshie8

so what do we have so far

50. Anikate

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

51. Anikate

yup

52. ganeshie8

how do you know there exists a SA ?

53. Anikate

no clue :(

54. ganeshie8

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

55. Anikate

the degree of the first exponent

56. ganeshie8

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

57. Anikate

numerator: 3 denominator: 2

58. ganeshie8

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

59. ganeshie8

knw how to find the SA ?

60. ganeshie8

simply do long division

61. ganeshie8

remember long division ?

62. Anikate

vaguely

63. Anikate

how do i do it for this?

64. ganeshie8

|dw:1434348039440:dw|

65. ganeshie8

|dw:1434348112918:dw|

66. Anikate

how do subtract the x and 12 x^2?

67. ganeshie8

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

68. ganeshie8

|dw:1434348365527:dw|

69. ganeshie8

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

oh cool! hot it! thanks!!

71. Anikate

got it*

72. ganeshie8

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

73. ganeshie8

what about x-int and y-int ?

74. Anikate

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

75. Anikate

@ganeshie8 is that right?

76. ganeshie8

doesn't look correct

77. ganeshie8

$$x=0$$ is a hole, so there are no y intercepts.

78. ganeshie8

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

79. ganeshie8

|dw:1434349091942:dw|

80. ganeshie8

|dw:1434349134532:dw|

81. ganeshie8

|dw:1434349181041:dw|

82. Anikate

so there could be infinite answers?

83. ganeshie8

|dw:1434349240955:dw|

84. ganeshie8

|dw:1434349306136:dw|

85. ganeshie8

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

86. ganeshie8

But $$x=0$$ is a hole, so discard that.

87. ganeshie8

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

88. ganeshie8

see if that makes more or less sense

89. Anikate

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

90. Anikate

@ganeshie8

91. ganeshie8

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

92. ganeshie8

setting y = 0, makes the denominator vanish

93. ganeshie8

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

94. Anikate

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

95. ganeshie8

tell me this, what exactly is an x intercept ?

96. Anikate

where the y=0

97. ganeshie8

explain more

98. Anikate

where the line on the graphs crosses the x-axis

99. ganeshie8

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

100. Anikate

yup

101. ganeshie8

|dw:1434350344473:dw|

102. ganeshie8

|dw:1434350374270:dw|