Symmetric about the origin

Hi all,

Can someone please help me understand how the following function is symmetric about the origin?

y = 3x /(x^2 + 9)

-y = 3(-x) / (-x)^2 + 9

-y = -3x / x^2 + 9 (multiply numerator and denominator by -1)

y = 3x/ -x^2 -9

The functions are not the same yet, in the back of my book it says that it is symmetric about the origin.

Thanks for the help,

Alex

Re: Symmetric about the origin

If the function is odd, then it is symmetric about the origin, i.e. .

Any function of the form:

where are constants and and are not both zero

is an odd function, since: