Manipulate function

Question

I'm trying to generate this simple graph using the Manipulate function

f[x_] := a x + b x^2;
Manipulate[Plot[f[x], {x, 0, 1}], {a, 0, 1}, {b, 0, 1}]

However, Mathematica doesn't return any graph! If instead of the above, I use now

Manipulate[Plot[a x + b x^2, {x, 0, 1}], {a, 0, 1}, {b, 0, 1}]

I can get what I wanted. Any thoughs on why the manipulate doesn't work with functions? Thanks!

This is covered in the "Possible Issues" section of the documentation for Manipulate. See example after Manipulate only "notices" explicit visible parameters — Bob Hanlon, Jun 30 '20 at 02:02

score 7 · Accepted Answer · answered Jun 29 '20 at 23:38

The problem is that you must pass a and b to the function. Try f[3] with your current definition and you get 3a + 9b which cannot be plotted. When using SetDelayed (:=), it cannot see that there is an a and b inside the function so it does not know where to assign the values. Instead, try this:

f[x_, a_, b_] := a x + b x^2
Manipulate[Plot[f[x, a, b], {x, 0, 1}], {a, 0, 1}, {b, 0, 1}]

Manipulate function

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