Finding the Y= of a Slant Asymptote given the Irrat. Poly...

[qbkr21]

f(x)=-9x^3+5x^2-5x-3/-7x^2+6x+7

I need to know:

The equation of the slant Asymptote in Y= form:?

What is the smallest value of x at which f(x) intersects its non-vertical asymptote: ?

Thanks for your help!!

 

[skeeter]

do the "real ugly" long division (I apologize for the line-up) ...

.................(9/7)x + (19/49)
.................----------------------------
-7x^2 + 6x + 7 | -9x^3  + 5x^2        - 5x  - 3
.................-9x^3 + (54/7)x^2 + 9x
.................----------------------------------
.......................(-19/7)x^2 - 14x - 3
.......................(-19/7)x^2 +(114/49)x
.......................---------------------------

slant asymptote is y = (9/7)x + (19/49)

set the slant asymptote = f(x) ... I solved it with a calculator. Damn if I'm gonna solve it by hand. x = -.35

question/comment ... where did this "problem" come from?
these are exactly the kind of problems that make relatively "easy" concepts very difficult. all they accomplish is frustration and helplessness. your instructor should be flogged for such an egregious abuse of assigning meaningful problems ... IMHO.

 

[qbkr21]

Thank you. I agree: many of the exercises we're doing are painful. However, I must figure them out to maintain my A average.

Thank you for your time and your insight. Obviously you are a very smart person!