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Parity


Date: 8/2/96 at 1:58:23
From: Alfred T Chu
Subject: Parity

Dear Dr. Math,

How do I determine if the following function is odd, even or 
neither? What is the symmetry of the graph?

        4    2      -1
k(x)= (x  + x   +1)

Thanks!  I hope you understand my problem and how I typed it.

Sincerely,

Alfred


Date: 8/6/96 at 10:56:53
From: Doctor Jerry
Subject: Re: Parity

Dear Alfred,

The function k(x) = (x^4+x^2+1)^(-1) is an even function since
k(x) = k(-x) for all x. This means the graph is symmetric about 
the y-axis.  

If, for example, (a,b) is on the graph, then so is (-a,b).  Why? 
Well, if (a,b) is on the graph, then b=k(a).  But, b=k(a)=k(-a).  
So, (-a,b) is on the graph.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra

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