# Odd / Even Functions.

• Sep 11th 2010, 01:48 PM
habibixox
Odd / Even Functions.
Hi, I have a test on pre calc topics on Monday in my Calc class.
I am reviewing odd and even functions right now.
Here is the problem: True or False: The function f(x)= x^-3 is an odd function.

I have true and this is what i did to prove it:

(-x)^-3 = -x since it equals -x it's odd right?

But then I graphed it on my graphing calculator and it did not look right O_o... am I doing something wrong? Can i be neither?
• Sep 11th 2010, 02:01 PM
yeKciM
Quote:

Originally Posted by habibixox
Hi, I have a test on pre calc topics on Monday in my Calc class.
I am reviewing odd and even functions right now.
Here is the problem: True or False: The function f(x)= x^-3 is an odd function.

I have true and this is what i did to prove it:

(-x)^-3 = -x since it equals -x it's odd right?

But then I graphed it on my graphing calculator and it did not look right O_o... am I doing something wrong? Can i be neither?

if function

$\displaystyle f(-x) = -f(x)$

function is odd.

if function

$\displaystyle f(-x) = f(x)$

function is even.

if function is

$\displaystyle f(-x) \neq f(x)$ and $\displaystyle f(-x) \neq -f(x)$ than function is neither odd neither even :D

$\displaystyle f(x) = x^{-3} = \frac {1}{x^3 }$

$\displaystyle f(-x) = - \frac {1}{x^3} = - f(x)$

so it's odd function :D

and here you are graph of that odd function :D