# Test Function for Symmetry

• Jan 22nd 2007, 04:09 PM
symmetry
Test Function for Symmetry
Test this function for symmetry:

f(x) = x^4 + x^² + 3
• Jan 22nd 2007, 04:59 PM
ThePerfectHacker
Quote:

Originally Posted by symmetry
Test this function for symmetry:

f(x) = x^4 + x^² + 3

The function has symmetty in the y-axis.
Because,
$f(-x)=(-x)^4+(-x)^2+3=x^4+x^2+3=f(x)$
• Jan 22nd 2007, 05:15 PM
symmetry
ok
So, basically we change x to -x, plug and chug?
• Jan 23rd 2007, 05:49 AM
topsquark
Quote:

Originally Posted by symmetry
So, basically we change x to -x, plug and chug?

Yup.
A function is called "even" if f(-x) = f(x). It is called "odd" if f(-x) = -f(x). Note that a function may be neither even nor odd.

-Dan
• Jan 23rd 2007, 08:00 AM
CaptainBlack
Quote:

Originally Posted by symmetry
So, basically we change x to -x, plug and chug?

No we think about what odd or even symmetry mean, then see if the
sample function has the property required.

Plug and chug implies just following rules. But that means you have to
remember a rule for each situation, which is a waste of valuable memory.

RonL