find where f(x) = 2x^2 / (x^2 + x + 1) crosses hor. asympt.

[zuuberbat]

1) Find the point where the graph of f crosses its horizontal asymptote.
f(x) = 2x^2 / x^2 + x + 1

-I don't know how to do this question at all, wasn't covered in class =/...

2) Find a rational function that satisfies the given conditions. There is no unique answer.

Given conditions:
vertical asymptote: x = 1
horizontal asymptote: y = -2
y-intercept: (0, -1)

-For this one, I know that in the function there has to be (x-1) to satisfy the vertical asymptote of x = 1. But I don't know what to do next..

Any help appreciated, thanks.

 

[arthur ohlsten]

Re: 2 Rational Function Questions..

y=2x^2/[x^2+x+1] improper fraction divide
y=2 -2[x+1]/[x^2+x+1]

horizontal assymptote at y=2 [2nd term goes to 0 as x-->oo]

set y=2
2=2 - [x+1] / [x^2+x+1]
0=[x+1]/[x^2+x+1]
0=x+1
x=-1 answer

y=-2 + k/[x-1]
horizontal assymptote = -2
vertical assymptote at x=1
when x=0 y=-1 substitute
-1=-2+k/[-1]
-1=-2-k
k=-1

y=-2- 1/[x-1] answer

Arthur

 

[Deleted member 4993]

Re: 2 Rational Function Questions..

1) Find the point where the graph of f crosses its horizontal asymptote.
f(x) = 2x^2 / x^2 + x + 1

-I don't know how to do this question at all, wasn't covered in class =/...

What is the equation of the horizontal asymptote?

for a quick review go to:

http://search.freefind.com/find.html?oq ... search=all


2) Find a rational function that satisfies the given conditions. There is no unique answer.

Given conditions:
vertical asymptote: x = 1
horizontal asymptote: y = -2
y-intercept: (0, -1)

-For this one, I know that in the function there has to be (x-1) to satisfy the vertical asymptote of x = 1.

That is not correct - please review conditions for vertical asymptote

http://search.freefind.com/find.html?id ... +asymptote

But I don't know what to do next..

Any help appreciated, thanks.