What Does the Graph of y=(x+1)/(x-1) Look Like?

[brandon26]

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

 

[LeonhardEuler]

This should help:
$$y=\frac{x+1}{x-1}$$
$$=\frac{(x-1)+2}{x-1}$$
$$=\frac{x-1}{x-1}+\frac{2}{x-1}$$
$$=1+\frac{2}{x-1}$$
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]

$$x+1=x-1+1+1=(x-1)+2$$

 

[brandon26]

oh right. Hehe, thanks.

 

[brandon26]

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