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

Any function of the form:

$\displaystyle f(x)=\frac{ax}{bx^2+c}$ where $\displaystyle a,b,c$ are constants and $\displaystyle a$ and $\displaystyle b$ are not both zero

is an odd function, since:

$\displaystyle f(-x)=\frac{a(-x)}{b(-x)^2+c}=-\frac{ax}{bx^2+c}=-f(x)$