## anonymous 4 years ago State the horizontal asymptote of the rational function. f(x) = x^2+6x-8/x-8

1. anonymous

Can you find the derivative of this function first?

2. anonymous

Set the derivative equal to zero

3. anonymous

i normally pluged it into the graph

4. anonymous
5. anonymous

All right, I'll assume you can't do that now. Is this the equation:$x ^{2}+\frac{ 6x-8 }{ x-8 }$

6. anonymous

i see what u posted @timo86m but idk what the horrizontal is

7. anonymous

@L.T. ok what would i do

8. anonymous

there is a slant retricemptote.. not a horizontal =/

9. anonymous

lol asymptote... lame chat =]

10. anonymous

the degree of the top is greater than the degree of the bottom therefore no horizontal asymptote no calc needed, that is all

11. anonymous

If what I wrote was the equation, then you find the derivative of each term in the equation, using the quotient rule on the second term.

12. anonymous

reall no horizontal ?

13. anonymous

if the degree of the bottom was greater, then the horizontal asymptote would be $$y=0$$ if the degree of the top is greater no horizontal asymptote

14. anonymous

yes there is a slant use long division

15. anonymous

if you ned to find the slant asymptote

16. anonymous

if the degrees are the same, it is the ration of the leading coefficients that is it

17. anonymous

so the anserw is no horizontal asymptote

18. anonymous

that is correct. there is none

19. anonymous

it has a slanted asymptote with a slope of 1045/1058

20. anonymous

ok thank you so much

21. anonymous

how'd you find that @timo86m

22. anonymous

take derivitive of (x^2+6x-8)/(x-8) ${\frac {2\,x+6}{x-8}}-{\frac {{x}^{2}+6\,x-8}{ \left( x-8 \right) ^{2} }}$ then just plug in a very high or very low value for x It has roughly a V asymptote of 8.5

23. anonymous