Similar Graphs

Date: 12/11/95 at 18:35:57
From: Anonymous
Subject: Graphing Equations

Dr. Math

I am a junior in high school.  I'm studying for my semester 
exam, but I need some help.  How would you describe how the two 
graphs of y = one over the square root of x squared and y = one over 
the square root of x squared minus 4 are similar and dissimilar?  
Most importantly, why does the second graph look as it looks?

Thanks for your help.
- Billy Feger    

Date: 6/13/96 at 20:32:31
From: Doctor Jim
Subject: Re: Graphing Equations

The graphs should look pretty much the same except the asymptote for 
the first one is the y-axis, because when x=0 the function is undefined, 
and for the second one the asymptotes are at 2 and -2, which again makes 
the denominator 0, so the function is undefined.  

Also, note that for numbers between -2 and 2 the argument of the 
radical is negative, so there are no real values of y, which is why 
there are no points graphed.

-Doctor Jim,  The Math Forum