Test y = 4x^2/x^2 + 1 for symmetry. Solution y =4x2/(x2+1) for symmetry about y axis: put -x in place of x y=4(-x)2/((-x)2+1) y=4x2/(x2+1) we get same equation. so curve is symmetric about y axis for symmetry about x axis put -y in place of y: -y =4x2/(x2+1) equation is not same as original one so not symmetric about x axis for symmetry about origin put -y in place of y:, -x in place of x -y =4(-x)2/((-x)2+1) -y =4(x)2/(x2+1) equation is not same as original one so not symmetric about origin.