# Thread: polynomial doesn't have horizontal asymptote?

1. ## polynomial doesn't have horizontal asymptote?

I need to find a horizontal of f(x)=3x^2+6x-10.
but my answer is there is no horizontal asymptote in the function 3x^2+6x-10 but i don't know how to explain why there is no horizontal asymptote.
can anyone explain for me please?

2. it is a parabola of the form (x - h)^2 = 4a(y - k), opening upward.

thus, no horizontal asymptotes.

see graph

3. Originally Posted by haebin
i don't know how to explain why there is no horizontal asymptote. can anyone explain for me please?
If they gave you rules for asymptotes, then you should need only to say something along the lines of "this polynomial function, not being a rational function, does not fulfill the requirements, listed on page (insert the page number here) for having a horizontal asymptote".

That should be an acceptable answer.

4. Originally Posted by haebin
I need to find a horizontal of f(x)=3x^2+6x-10.
but my answer is there is no horizontal asymptote in the function 3x^2+6x-10 but i don't know how to explain why there is no horizontal asymptote.
can anyone explain for me please?
Analyze the following:

$\lim_{x\to\infty}3x^2+6x-10$ and $\lim_{x\to-\infty}3x^2+6x-10$

If the limits are finite, then a horizontal asymptote may exist.

If not, then it doesn't have one.