# Thread: Test Function for Symmetry

1. ## Test Function for Symmetry

Test this function for symmetry:

f(x) = x^4 + x^² + 3

2. 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,
$f(-x)=(-x)^4+(-x)^2+3=x^4+x^2+3=f(x)$

3. ## ok

So, basically we change x to -x, plug and chug?

4. 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

5. 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