Asymptotes of functions .Help me please!

Question

The equation of the oblique asymptote is y=kx+b. I have a function f(x)=(x^2+4)/sqr(x^2-4). I get  the b infinite. Am I right or not? I am stuck in this. And I dont know how to wirte the equation. 

Answer 1

y=x is slant asymptote for right branch, y=-x for left.

 

Try:

y = [x²(1+4/x²)] / sqrt [x²(1 - 4/x²)]

 

But the square root of the x² in the denominator can be pulled out from under the radical as |x|. As x gets very large y approaches x²/|x|.

 

Try visiting https://www.desmos.com/calculator to graph the function along with the slant asymptotes and you will see.