Question

find the horizontal asymptote of the graph of y=-2x^6+5x+8/8x^6+6x+5

Answer 1

ignore all terms except the highest order term in the top and bottom
then find the ratio of those two terms.

Answer 2

how do i do that?

Answer 3

@thesecretstoday?

Answer 4

Divide up and down by x^6 to obtain
\[\Large
\frac{-2 x^6+5 x+8}{8 x^6+6 x+5}=\frac{-2
x^6+5 x+8}{\frac{x^6 \left(8 x^6+6
x+5\right)}{x^6}}=\frac{\frac{8}{x^6}+\frac{5}{x^5}-2}{\frac{5}{x^6}+\frac{6}{x^5}
+8}
\]
If x goes to infinity, what is the limit of the ratio?

Answer 5

The limit goes to
\[
\frac {0 + 0 -2}{0+0+8}=-\frac 2 8 =-\frac 1 4
\]
so y= 1/4 is your vertical asymptote.

Answer 6

uhhhh sooo is the horizontal the same thing?

Answer 7

Yes