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|dw:1434344992559:dw|

how do u know those x and y ints?

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

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|

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|

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