Thread: 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?

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

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

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

so it's odd function


and here you are graph of that odd function