Question regarding asymptotes with a composite function?

[captainoats]

Evening all,

I have the equation:



So I know that there is an asymptote at x=-3, as you can't divide by zero.

But, how do you go about working out the y asymptote manually? I know that you can plug it into the calulator and work it out, but I don't understand how I would tackle this if I don't have my calculator.

Thanks!  

[TrueTears]

Long divide it, this yields

Hence y asy at y = 1

code for fractions

\frac{ }{ }

[captainoats]

Long divide it, this yields

Hence y asy at y = 1

code for fractions

\frac{ }{ }

Awesome! Thankyou!

[dcc]

A trick which I picked up off VN a long, long time ago was to consider rewriting the equation, as follows:



It's very simple.  Another example would be:



Very useful, in my opinion

[captainoats]

A trick which I picked up off VN a long, long time ago was to consider rewriting the equation, as follows:



It's very simple.  Another example would be:



Very useful, in my opinion

Wow! That's sweet! It took me a while to see what was happening.. (long day!)... but that is really cool!

[kamil9876]

A trick which I picked up off VN a long, long time ago was to consider rewriting the equation, as follows:



It's very simple.  Another example would be:



Very useful, in my opinion

Very cool indeed, you can use this to prove the long division algorithm (ie: if you avoid rewriting the redundant parts such as the denominator etc. and just extract the numbers that you are actually manipulating you get that algorithm )

Lol i always forget that algorithm so i stick to this, even for cubics over quadratics, which can get tedious

[Mao]

A less rigorous way can get you the answer faster:

as , , ,

as , , ,

(basically ignore the constant)

[dcc]

That might get you the constant term, however to find the other term its still equivalent to solving:



Which is essentially the process I outlined above, done in a semi-reversed fashion.

[Gloamglozer]

A trick which I picked up off VN a long, long time ago was to consider rewriting the equation, as follows:



It's very simple.  Another example would be:



Very useful, in my opinion

With the second example, can you please explain how you got to ?

[TrueTears]

Because the denominator is 2x+3 and the number is x+2 you need ask yourself "How do I get a 2x+3 on the top so when I split the fraction they can cancel"

So to get a coefficient of 2 in front of the x, we put a 2 in front of it but then we must multiply (x+2) by , the net result is still the same for the coefficient of x.

But now we have instead of 2, so what do we need to do to to make it into a 2? We add hence net result is still 2.

EDIT: too fast shinny

[shinny]

EDIT: too fast shinny

Nah deleted my post =P I actually didn't realise he 'artificially' made the 2x+3 and just explained how he cancelled it out to be 1/2. Read TT's explanation =T

[kamil9876]

Another way to do it if you aren't sure:

[/0]

It's good for simple examples but with complicated examples I would just go with long division, which is a sure thing, instead of wasting time thinking of how to split it up.

[Gloamglozer]

Thanks for the explanation TT and kamil (and shinny even though I didn't read your post lol).

I understand it now. 

[shinny]

Thanks for the explanation TT and kamil (and shinny even though I didn't read your post lol).

I understand it now. 

Heh ignore mine. Misunderstood what you were misunderstanding and answered something retardedly basic =P