The curve \(C\) has equation \(y = \frac{x+1}{x^2+3}\).

1. Show that \(C\) has no vertical asymptotes and state the equation of the horizontal asymptote. [2]
2. Find the coordinates of any stationary points on \(C\). [4]
3. Sketch \(C\), stating the coordinates of the intersections with the axes. [3]
4. Sketch \(y^2 = \frac{x+1}{x^2+3}\), stating the coordinates of the stationary points and the intersections with the axes. [4]