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

Thread starter brandon26
Start date Sep 10, 2005
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Graph

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The graph of y=(x+1)/(x-1) resembles a hyperbola, characterized by a vertical asymptote at x=1 and a horizontal asymptote at y=1. It can be rewritten as y=1 + 2/(x-1), indicating a transformation of the basic hyperbola y=1/x, shifted up by one and left by one. The discussion also touches on simplifying the expression y=(1+2x)/(1-x), though specific simplification steps are not provided. Understanding these transformations is key to accurately sketching the graph. Overall, the conversation centers on the graphical representation and manipulation of rational functions.

Sep 10, 2005

brandon26

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

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Sep 10, 2005

LeonhardEuler

Gold Member

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.

Sep 10, 2005

brandon26

Where does the +2 come from?

Last edited: Sep 10, 2005

Sep 10, 2005

LeonhardEuler

Gold Member

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

Sep 10, 2005

brandon26

oh right. Hehe, thanks.

Sep 10, 2005

brandon26

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

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