# On finding total number of non linear asymptotes

So i understood how to obtain non linear asymototes of a function if any. So how do you know if the function has more than one non linear asymptote? I mean look at the part of the graph "in the 3rd quadrant". How do i know it wont have any non linear asymptote "there"?

Here is the reference Question used on all my posts:

y =$$(x^3+2x+9)$$/$$(sqrt(4x^2+3x+2))$$

My asymptote obtained using long division

y=(x^2/2) -(3x/16) +(9/128)

Graph:

Red line: Original Function

Black line: Asymptote

• I am planning to learn mathsjax next. – user33699 Jul 27 '17 at 8:31
• Most of mathjax $\equiv$ putting $ around mathematical objects – Shuri2060 Jul 27 '17 at 8:32 • Not sure on how to answer. There are an infinite number of possible non-linear asymptotes in the example you've given (and the same for a lot of other examples too). – Shuri2060 Jul 27 '17 at 8:36 • How do you find an asymptote for the graph of the function in the "negetive part". – user33699 Jul 27 '17 at 8:38 • I'm not sure how you got it for the positive part, but surely using the same method while applying the idea$x\to-\infty$instead of$x\to\infty\$ will work? – Shuri2060 Jul 27 '17 at 8:40