Question 125464
(a) given f(x) = (2x+3)/(x+2)

To get the vertical asymptote, set the denominator to 0
==> x+2 = 0
==> x = -2 is the equation of the vertical asymptote.
Now divide all the terms of the function by x and set lt x-> infinity.

==> f(x) = (2 + 3/x)/ (1 + 2/x)
AS x -> infinity, we have f(x) = 2/1 = 2
Thus y = 1 is the equation of the horizontal asymptote.

(b)As x^2 + 1 = 0 does not have a real solution, there is no vertical asymptote.
Divide each term by x^2 and setting lt x-> 0, we get y = 0
So y = 0 is the equation of the horizontal asymptote.

good luck!!!