Beware!!! Many answers possible.
•#(5x^2)/(x^2 + 4)#
This example will have a horizontal asymptote at #y = 5# (since the ratio between the highest degrees #=# 5) and no vertical asymptote (since if #x^2 + 4 = 0 -> x^2 = -4 -> x = O/#).
You will have a horizontal asymptote at #y = 5# anytime that the degree of the denominator equals that of the numerator and the ratio between the numerator and the denominator equals #5#. If that is the only asymptote, the denominator when set to #0# like in the example above needs to have no solution; otherwise there will be vertical asymptotes.
Practice exercises:
#1#. Determine an equation for a rational function with a horizontal asymptote at #y = -2#
#2.# Determine an equation for a rational function with vertical asymptotes at #x = -3# and #x = 5# and a horizontal asymptote at #y = 7#.
Hopefully this helps, and good luck!
