hi i make drafts in order to be sure that i am ok with the basics cirously, this manipulate doesn't work for me :

ClearAll[a, b, x, f]
f[x_] := (a x^2)/(b + x)
Plot[
 {f[x], 10} /. {a -> 10.0, b -> 5.0},
 {x, -60, 60}, 
 PlotRange -> {-60, 60}
 ]

Manipulate[
 Plot[f[x], {x, -10, 10}, PlotRange -> {-20, 20}],
 {a, -4, 4}, {b, -4, 4}]
Manipulate[
 Plot[f[x], {x, -10, 10}, PlotRange -> {-20, 20}],
 {a, 1, 10}, {b, 0, 2 \[Pi]}
 ]

i dont understand why does the Plot[] work but the both Manipulate[] display a x-range from -1.0 to 1.0 which is not what i expect and the curve is not visible, only the axes. thanks for your help...