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:
Vertical:
b) g(x)=3x/x^2+4
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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Cheers,
Stan H.
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