Anikate
  • Anikate
find hole, HA, SA, VA, x-int, and y-int. Posting question. please help.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Anikate
  • Anikate
|dw:1434344992559:dw|
UsukiDoll
  • 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
Anikate
  • Anikate
how do u know those x and y ints?

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UsukiDoll
  • 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
Anikate
  • Anikate
oh lol sorry didnt notice, im just as fried XD 1:13AM here
Anikate
  • Anikate
ok, after factorign out x's, what now?
UsukiDoll
  • UsukiDoll
brain hurts x.x
Anikate
  • Anikate
i feel ya. u live in USA?
UsukiDoll
  • UsukiDoll
yup
Anikate
  • Anikate
east coast?
UsukiDoll
  • UsukiDoll
you must live in the east coast. I'm 6 hours behind you
Anikate
  • Anikate
yup
UsukiDoll
  • UsukiDoll
it's only 7:16 pm in my state
Anikate
  • Anikate
mann lucky you!
Anikate
  • Anikate
so how do u find hole, VA, HA, SA?
UsukiDoll
  • UsukiDoll
I am ... tired...so sorry @ganeshie8 take over xD
Anikate
  • Anikate
kk np
ganeshie8
  • ganeshie8
|dw:1434345612001:dw|
ganeshie8
  • ganeshie8
set the denominator equal to \(0\) to get VA/holes
Anikate
  • Anikate
ok
Anikate
  • Anikate
SA?
ganeshie8
  • ganeshie8
First find VA/holes, show ur work so that i know u got it
Anikate
  • Anikate
oh ok
Anikate
  • Anikate
|dw:1434345921379:dw|
Anikate
  • Anikate
@ganeshie8
ganeshie8
  • ganeshie8
why are you plugging in 0 in place of x ? |dw:1434346170455:dw|
ganeshie8
  • ganeshie8
For VA/holes you simply need to set the denominator equal to 0 and solve x |dw:1434346189911:dw|
Anikate
  • Anikate
ooh waitI got it, sorry my brain is half dea. ill do the work again
Anikate
  • Anikate
|dw:1434346226956:dw|
ganeshie8
  • ganeshie8
Yes, so x=0 and x=4 are discontinuities you need to figure out which of them are holes and VAs
Anikate
  • Anikate
how do i do that?
ganeshie8
  • ganeshie8
do you know how to tell whether a discontinuity is a hole or a VA ?
Anikate
  • Anikate
no....
ganeshie8
  • ganeshie8
Okay, it is easy. look at the given rational expression |dw:1434346474036:dw|
ganeshie8
  • ganeshie8
The factor \(\large x\) is common to both numerator and denominator. Therefore \(x=0\) is a hole
ganeshie8
  • ganeshie8
the factor \((x-4)\) is not there in the numerator, so \(x=4\) is a VA
Anikate
  • 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?
ganeshie8
  • ganeshie8
do you see \(x\) is there in both numerator and denominator but \(x-4\) is there only in the denominator ?
Anikate
  • Anikate
yes
ganeshie8
  • ganeshie8
Since the factor \(x\) cancels out, \(x=0\) is a hole.
Anikate
  • Anikate
ok
ganeshie8
  • ganeshie8
Since the factor \(x-4\) does not cancel out, so \(x-4=0\) is a VA.
ganeshie8
  • ganeshie8
Notice that \(x-4=0\) is same as \(x=4\)
Anikate
  • Anikate
oh ok
ganeshie8
  • ganeshie8
basically you need to see what factors are common to both numerator and denominator for holes
Anikate
  • Anikate
so VA is just the denominator after the entire equation is simplified?
ganeshie8
  • ganeshie8
Yes
Anikate
  • Anikate
ok, and how about SA?
ganeshie8
  • ganeshie8
so what do we have so far
Anikate
  • Anikate
hole: x=0 VA: X=4 SA: ?
Anikate
  • Anikate
yup
ganeshie8
  • ganeshie8
how do you know there exists a SA ?
Anikate
  • Anikate
no clue :(
ganeshie8
  • ganeshie8
do you know how to tell the degree of a polynomial ?
Anikate
  • Anikate
the degree of the first exponent
ganeshie8
  • ganeshie8
Yes, look at the given rational expression again. Degree of numerator = ? Degree of denominator = ?
Anikate
  • Anikate
numerator: 3 denominator: 2
ganeshie8
  • ganeshie8
Yes! degree of numerator is just 1 greater than the degree of denominator so there exists a SA
ganeshie8
  • ganeshie8
knw how to find the SA ?
ganeshie8
  • ganeshie8
simply do long division
ganeshie8
  • ganeshie8
remember long division ?
Anikate
  • Anikate
vaguely
Anikate
  • Anikate
how do i do it for this?
ganeshie8
  • ganeshie8
|dw:1434348039440:dw|
ganeshie8
  • ganeshie8
|dw:1434348112918:dw|
Anikate
  • Anikate
how do subtract the x and 12 x^2?
ganeshie8
  • ganeshie8
Oh yes, we cant subtract apples and coconuts, so we just leave it as it is : |dw:1434348286262:dw|
ganeshie8
  • ganeshie8
|dw:1434348365527:dw|
ganeshie8
  • ganeshie8
we're done because when you subtract you will get a remainder whose degree is less than the denominator., so the SA is \[\large y=3x+12\]
Anikate
  • Anikate
oh cool! hot it! thanks!!
Anikate
  • Anikate
got it*
ganeshie8
  • ganeshie8
good, notice that there wont be any HA because the degree of numerator is high
ganeshie8
  • ganeshie8
what about x-int and y-int ?
Anikate
  • Anikate
ok and the x-in, y-int is y-int: 0 x-int: 0
Anikate
  • Anikate
@ganeshie8 is that right?
ganeshie8
  • ganeshie8
doesn't look correct
ganeshie8
  • ganeshie8
\(x=0\) is a hole, so there are no y intercepts.
ganeshie8
  • ganeshie8
for x intercepts, you set y = 0|dw:1434349076055:dw|
ganeshie8
  • ganeshie8
|dw:1434349091942:dw|
ganeshie8
  • ganeshie8
|dw:1434349134532:dw|
ganeshie8
  • ganeshie8
|dw:1434349181041:dw|
Anikate
  • Anikate
so there could be infinite answers?
ganeshie8
  • ganeshie8
|dw:1434349240955:dw|
ganeshie8
  • ganeshie8
|dw:1434349306136:dw|
ganeshie8
  • ganeshie8
the solutions when setting the numerator to 0 are : \(\large x = 0,~\frac{1}{\sqrt{3}},~-\frac{1}{\sqrt{3}}\)
ganeshie8
  • ganeshie8
But \(x=0\) is a hole, so discard that.
ganeshie8
  • ganeshie8
The x intercepts are : \(\large \frac{1}{\sqrt{3}},~~-\frac{1}{\sqrt{3}}\)
ganeshie8
  • ganeshie8
see if that makes more or less sense
Anikate
  • Anikate
sorry, slow internet. so the x-intercepts matters on the numerator??
Anikate
  • Anikate
@ganeshie8
ganeshie8
  • ganeshie8
Notice, x intercepts are points on x axis so the y value will be 0
ganeshie8
  • ganeshie8
setting y = 0, makes the denominator vanish
ganeshie8
  • ganeshie8
so yes, in that sense only the numerator matters for x intercepts
Anikate
  • Anikate
how? can we just set x to 0 and get y=0 as an answer?
ganeshie8
  • ganeshie8
tell me this, what exactly is an x intercept ?
Anikate
  • Anikate
where the y=0
ganeshie8
  • ganeshie8
explain more
Anikate
  • Anikate
where the line on the graphs crosses the x-axis
ganeshie8
  • ganeshie8
Exactly! when the curve intersects the x axis, the y value will be 0, yes ?
Anikate
  • Anikate
yup
ganeshie8
  • ganeshie8
|dw:1434350344473:dw|
ganeshie8
  • ganeshie8
|dw:1434350374270:dw|