Given the following rational function

Question

Given the following rational function, find
a. the horizontal asymptote(s),
b. the vertical asymptote(s), if any, and
c. the oblique asymptote(s), if any.
f(x)=x^2+3x+2/x+2

Answer 1

f(x) = (x+1)(x+2)/(x+2)

a. There is no horizontal asymptote(s) since the numerator is one degree higher than the denominator, which means an oblique asymptote exist.

b. There is no vertical asymptote(s) since as x -> -2, y -> -1.

c. The oblique asymptote is y = x+1.