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

- Anikate

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

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- Anikate

|dw:1434344992559:dw|

- 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

how do u know those x and y ints?

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## More answers

- 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

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

- Anikate

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

- UsukiDoll

brain hurts x.x

- Anikate

i feel ya. u live in USA?

- UsukiDoll

yup

- Anikate

east coast?

- UsukiDoll

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

- Anikate

yup

- UsukiDoll

it's only 7:16 pm in my state

- Anikate

mann lucky you!

- Anikate

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

- UsukiDoll

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

- Anikate

kk np

- ganeshie8

|dw:1434345612001:dw|

- ganeshie8

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

- Anikate

ok

- Anikate

SA?

- ganeshie8

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

- Anikate

oh ok

- Anikate

|dw:1434345921379:dw|

- Anikate

@ganeshie8

- ganeshie8

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

- ganeshie8

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

- Anikate

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

- Anikate

|dw:1434346226956:dw|

- ganeshie8

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

- Anikate

how do i do that?

- ganeshie8

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

- Anikate

no....

- ganeshie8

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

- ganeshie8

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

- ganeshie8

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

- 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

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

- Anikate

yes

- ganeshie8

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

- Anikate

ok

- ganeshie8

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

- ganeshie8

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

- Anikate

oh ok

- ganeshie8

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

- Anikate

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

- ganeshie8

Yes

- Anikate

ok, and how about SA?

- ganeshie8

so what do we have so far

- Anikate

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

- Anikate

yup

- ganeshie8

how do you know there exists a SA ?

- Anikate

no clue :(

- ganeshie8

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

- Anikate

the degree of the first exponent

- ganeshie8

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

- Anikate

numerator: 3
denominator: 2

- ganeshie8

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

- ganeshie8

knw how to find the SA ?

- ganeshie8

simply do long division

- ganeshie8

remember long division ?

- Anikate

vaguely

- Anikate

how do i do it for this?

- ganeshie8

|dw:1434348039440:dw|

- ganeshie8

|dw:1434348112918:dw|

- Anikate

how do subtract the x and 12 x^2?

- ganeshie8

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

- ganeshie8

|dw:1434348365527:dw|

- 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

oh cool! hot it! thanks!!

- Anikate

got it*

- ganeshie8

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

- ganeshie8

what about x-int and y-int ?

- Anikate

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

- Anikate

@ganeshie8
is that right?

- ganeshie8

doesn't look correct

- ganeshie8

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

- ganeshie8

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

- ganeshie8

|dw:1434349091942:dw|

- ganeshie8

|dw:1434349134532:dw|

- ganeshie8

|dw:1434349181041:dw|

- Anikate

so there could be infinite answers?

- ganeshie8

|dw:1434349240955:dw|

- ganeshie8

|dw:1434349306136:dw|

- ganeshie8

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

- ganeshie8

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

- ganeshie8

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

- ganeshie8

see if that makes more or less sense

- Anikate

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

- Anikate

@ganeshie8

- ganeshie8

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

- ganeshie8

setting y = 0, makes the denominator vanish

- ganeshie8

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

- Anikate

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

- ganeshie8

tell me this, what exactly is an x intercept ?

- Anikate

where the y=0

- ganeshie8

explain more

- Anikate

where the line on the graphs crosses the x-axis

- ganeshie8

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

- Anikate

yup

- ganeshie8

|dw:1434350344473:dw|

- ganeshie8

|dw:1434350374270:dw|