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

Thread starter brandon26
Start date Sep 10, 2005
Tags

Graph

AI Thread Summary

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?

Physics news on Phys.org

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)

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .

View full post »

Thread 'I've come across another fluid pressure problem I don't understand'

Neglect gravity other than that of water; neglect friction. F1=ρgsh=1000*10*1*(1+4)=50000 N; F1=ρgsh=1000*10*0.1*4=4000 N; F3=50000-4000=46000 N?

View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

View full post »