given the following rational function

Question

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

Answer 1

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.