Question

Test for origin symmetry:
y=x/(x^2+1)

Answer 1

$y=\dfrac{x}{x^2+1}\\\\ -y=-\dfrac{-x}{(-x)^2+1}\\ -y=\dfrac{x}{x^2+1}\\ y=-\dfrac{x}{x^2+1}$

$-\dfrac{x}{x^2+1}\not =\dfrac{x}{x^2+1}$ so it's not symmetrical about the origin.