Question 137344
Find the equations for the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote. 
a) f(x)=2x+1/x-4 
Answer:
Horizontal: as x goes to +inf, f(x) goes to 2x/x = 2
So, horizontal asymptote is y = 2
-------------------------------------
Vertical: 
f(x) is undefined at x=4
So, vertical asymptote at x=4
------------------------
b) g(x)=3x/x^2+4 
HA: as x goes to infinity f(x) goes to 0x^2/x^2 = 0
So horizontal asymptote is y=0
-----------------
VA:g(x) is never undefined because x^2+4 is always > 0
So, no vertical asymptotes.
==================================
Cheers,
Stan H.