Graphs

brandon26

Could anyone show me what the graph of y=(x+1)/(x-1) looks like?

LeonhardEuler

This should help:
[tex]y=\frac{x+1}{x-1}[/tex]
[tex]=\frac{(x-1)+2}{x-1}[/tex]
[tex]=\frac{x-1}{x-1}+\frac{2}{x-1}[/tex]
[tex]=1+\frac{2}{x-1}[/tex]
So it is the graph of y=1/x, just multiplied by two, shifted up by one, and shifted to the left by one.

brandon26

Where does the +2 come from?

LeonhardEuler

[tex]x+1=x-1+1+1=(x-1)+2[/tex]

brandon26

oh right. Hehe, thanks.

brandon26

How would simplify y=(1+2x)/(1-x)