Question 43101
Is the following symmetric with respect to the x axis, y axis, origin, or no symmetry? 
y= (1)/(x^2 + 1)

f(x)= 1/(x^2+1)
f(-x)=1/((-x)^2+1) = 1/x^2+1
-f(-x)= -1/((-x)^2+1)= -1/(x^2+1)

Since f(x) = f(-x) you have y-axis symmetry.
Since f(x) is not equal to -f(-x) you do not have origin symmetry.
Since y does not equal -y you do not have x-axis symmetry.

Cheers,
stan H.