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

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

Mathematics
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|dw:1434344992559:dw|
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
how do u know those x and y ints?

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Other answers:

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

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