Associated Topics || Dr. Math Home || Search Dr. Math

### 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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search