What is the horizontal asymptote of the graph of #y=(3x^6-7x+10)/(8x^5+9x+10)#?

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What is the horizontal asymptote of the graph of #y=(3x^6-7x+10)/(8x^5+9x+10)#?

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Answer 1 · 2014-12-29T19:57:15

Well, I do not think that this function has a horizontal asymptote...

If you evaluate the limits at #oo# you get:
#lim_(x->oo)f(x)=oo# and
#lim_(x->-oo)f(x)=-oo#

The general form of your graph should be:
enter image source here
The graph does not pass through the origin (when #x=0, y=1#), and near the origin you have:

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What is the horizontal asymptote of the graph of #y=(3x^6-7x+10)/(8x^5+9x+10)#?

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