Curve sketching Q: hor. asymptote of y = (2 + x) / (1 - x)

[Guest]

I started my homework and got stuck on the first question.

I need to sketch y = (2 + x) / (1 - x), and I can't figure out the horizontal asymptote.
So far, I have a limit as x goes to +/- infinity set up, but it gives me 2 instead of -1.
Can someone please point me in the right dierection?

Thank you for your time.

 

[hypoid]

Lim _x->±inf (2 + x) / (1 - x)

Divide the top and bottom by x to get:

Lim _x->±inf (2/x + 1) / (1/x - 1)

. . .= Lim _x->±inf (0 + 1) / (0 - 1)

. . .= -1