Question

State the horizontal asymptote of the rational function.

f(x) = x^2+6x-8/x-8

Answer 1

Can you find the derivative of this function first?

Answer 2

Set the derivative equal to zero

Answer 3

i normally pluged it into the graph

Answer 4

https://www.google.com/search?q=x%5E2%2B6x-8%2Fx-8&rlz=1C1CHFX_enUS470US470&oq=x%5E2%2B6x-8%2Fx-8&sugexp=chrome,mod=11&sourceid=chrome&ie=UTF-8#hl=en&safe=off&rlz=1C1CHFX_enUS470US470&sclient=psy-ab&q=(x%5E2%2B6x-8)%2F(x-8)&oq=(x%5E2%2B6x-8)%2F(x-8)&gs_l=serp.3...2141.18850.1.19323.8.8.0.0.0.0.120.792.5j3.8.0.les%3B..0.0...1c.1.Q4G1o6RnZBs&psj=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=35197abecd6f379b&biw=1422&bih=776

Answer 5

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

Answer 6

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

Answer 7

@L.T. ok what would i do

Answer 8

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

Answer 9

lol asymptote... lame chat =]

Answer 10

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

Answer 11

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.

Answer 12

reall no horizontal ?

Answer 13

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

Answer 14

yes there is a slant use long division

Answer 15

if you ned to find the slant asymptote

Answer 16

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

Answer 17

so the anserw is no horizontal asymptote

Answer 18

that is correct. there is none

Answer 19

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

Answer 20

ok thank you so much

Answer 21

how'd you find that @timo86m

Answer 22

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

Answer 23

My bad; must have misread the question :(