Limits at Infinity? sketch y = 3 + 2/x using extrema, asympt

[jml14]

I'm suppose to sketch a graph of the function using extrema, intercepts, symmetry, and asymptotes.

y = 3 + 2/x

Here is what I did, but I was told was wrong so I got confused.

lim 3 + lim 2/x -> 3 + 0 = 3


Help Please!

 

[royhaas]

Re: Limits at Infinity???

There is a horizontal asymptote at \(\displaystyle y=3\). There's no extrema, intercepts or symmetry. The graph is a hyperbola shifted upward by 3 units.

 

[BigGlenntheHeavy]

Re: Limits at Infinity???

Extrema: None
Intercepts: (-2/3,0)
Symmetry: Yes
Asymptotes: x = 0, y = 3