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. =-f(x))
.
Any function of the form:
=\frac{ax}{bx^2+c})
where 
are constants and 
and 
are not both zero
is an odd function, since:
=\frac{a(-x)}{b(-x)^2+c}=-\frac{ax}{bx^2+c}=-f(x))
