Find the horizontal asymptote (if any) of the graph of the following function.
y= -6x^4-x+6/3x^6-7x+6
please help

Question

Find the horizontal asymptote (if any) of the graph of the following function.
y= -6x^4-x+6/3x^6-7x+6
please help

anonymous · Answer

Try to think about what happens if you put in a large value for $x$, say, $x=10^6$.
On top, you'd get $-6*10^{24}-10^6+6 $which is really close to $-6*10^{24}$.
On the bottom, we similarly get something really close to $3*10^{36}$.
Then the whole fraction is very close to 
$$\frac{-6*10^{24}}{3*10^{36}}=\frac{-2}{1000000000000}.$$

I hope the point I'm trying to make is clear.

anonymous · Answer

i dont really understand couldnt the 6's cancel?

anonymous · Answer

They actually don't because we can only cancel multiplicative factors in fractions. Let me see if I can find a link to the method I was attempting to illustrate.

anonymous · Answer

Ah, here's a nice summary of the properties of rational functions: https://people.richland.edu/james/lecture/m116/polynomials/rational.html

anonymous · Answer

alright ty man im pretty sure i can do it now