Link the discriminant interval to the missing horizontal levels

C has equation $y=(x^2+9x+16)/(x+2)$.

(i) Find its asymptotes.

(ii) Find, in exact form, all k for which $k=(x^2+9x+16)/(x+2)$ has no real roots.

(iii) Sketch C with asymptotes, stationary points and x-/y-axis intersections labelled.