Posted by **anon** on Wednesday, December 21, 2011 at 10:44am.

given the following rational function

a. state the domain

b. find the vertical and horizontal asymptotes if any

c. find the oblique asymptote

f(x) = x^2 + 7x + 5 / x + 8

- pre calculus -
**Steve**, Wednesday, December 21, 2011 at 11:36am
as usual, the domain is all reals except where the denominator is zero. That is, all reals except x = -8

Vertical asymptotes occur when the denominator is zero and the numerator is not.

at x = -8, the numerator is not zero, so that's the vertical asymptote.

For large x, f(x) is just x^2/x = x, so there's an oblique asymptote at the line y=x, and here are no horizontal asymptotes.

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