Question 43101
You can just test values.  If it is symmetric wrt (with respect to) the x-axis, then a value of y will give you the same x as -y.  If it is symmetric wrt the y-axis, a value for x will give you the same y as -x.  And if it is symmetric wrt the origin, then (x,y) will become (-x,-y).
So, let's test each.  If we plug in any x and any -x, the corresponmding y will be the same because x only appears once in this equation, and it is x^2.  So this is symmetric wrt the y-axis.  If we try to do the same for y, we see that a negative value for y will have no corresponding x (since 1/(x^2 + 1) is always positive).  So this is not symmetric wrt the x-axis.  And finally, since it never goes below the x-axis, it cannot be symmetric wrt the origin.  So it symmetric only wrt the y-axis.