Convert string to function with an argument

Question

I am trying to build an expression by first writing it out as a string and then using ToExpression to convert it to an expression. However, I cannot figure out how to make expression recognize x as an argument. Here is my code building the expression:

functionbuilder := Module[{}, 
   functionstring = "B1";
   nosines = Input["How many sine curves?"];
   For[n = 2, n <= 3*nosines - 1, n = n + 3, 
      string=StringJoin["+B", ToString[n], "*Sin[B", ToString[n + 1],"*x+B",ToString[n+2],"]"];
      functionstring = StringJoin[functionstring, string]
   ];
   Return[ToExpression[functionstring]]
]

This returns exactly the expression I want. For example, when nosines=3, the output is:

B1 + B2 Sin[B4 + B3 x] + B5 Sin[B7 + B6 x] + B8 Sin[B10 + B9 x]

All I am looking for is how define this expression as a function with x as an argument. I have tried:

f[x_]:=functionbuilder[x]

But this does not work. What syntax do I need to define a new function f[x] from my expression? To be clear, I want to be able to evaluate the function f[2.] and get:

B1 + B2 Sin[2. B3 + B4] + B5 Sin[2. B6 + B7] + B8 Sin[B10 + 2. B9]

Answer 1

You can use Symbol[] to sidestep all that rigamarole with ToExpression[]:

With[{n = 3}, 
     B1 + Sum[Symbol["B" <> IntegerString[k - 1]]
              Sin[Symbol["B" <> IntegerString[k]] x +
                  Symbol["B" <> IntegerString[k + 1]]], {k, 3, 3 n, 3}]]
   B1 + B2 Sin[B4 + B3 x] + B5 Sin[B7 + B6 x] + B8 Sin[B10 + B9 x]

However, I see no justification for needing to generate so many symbols. One can just input a list of parameters if an undetermined number of them is needed, and just let the listability of the arithmetic operators and elementary functions take care of it:

1 + {2, 5, 8}.Sin[{3, 6, 9} x + {4, 7, 10}]
   1 + 2 Sin[4 + 3 x] + 5 Sin[7 + 6 x] + 8 Sin[10 + 9 x]