Question

What are the vertical asymptotes, horizontal asymptotes, slant asymptotes, and the holes of this equation:

(x^2-x+1)/(x-3)

Answer 1

you can't factor x^2-x+1, so there will be no removable discontinuities (so-called "holes"), so x=3 will be the vertical asymptote. take the limit as x goes to infinity, and you get y=1 as the horizontal asymptote. I'm not so sure about the slant one.

Answer 2

wait, are you sure that the horizontal asymptote is 1 because i thought that the horizontal asymptote was y=none.

Answer 3

yeah, nvm. y goes to infinity.

Answer 4

to find a horizontal asymptote, do polynomial long division. y=x+2 should be the slant asymptote.

Answer 5

ok thank you!
Do you think you could find the holes and slant asymptotes for this equation:(x^2-9x+20)/(2x^2-8x)