Function with Dynamic parameter gives an empty plot

Question

I have a function which depends on three parameters, and I would like to see how it changes as I vary those. I created three sliders, used Dynamic and what I obtain seems to work, in the sense that indeed the function outputs values which are correct and are updated in real-time if I move the sliders.

The problem is that there is no way for me to plot those values. I tried in many different ways (with Dynamic inside or outside, with Evaluate): nope. Why can't I plot a function which correctly returns values?

{"A", Slider[Dynamic[A]], Dynamic[A*100]}
{"α", Slider[Dynamic[α]], Dynamic[α*100]}
{"β", Slider[Dynamic[β]], Dynamic[β + 1]}
σ[ϵ_] = 
 Dynamic[A*100*(Exp[α*100*ϵ] - 1)/(1 + 
      Exp[(β + 1)*α*100*ϵ])]
σ[.001]
Plot[σ[ϵ], {ϵ, 0, 1}]

Answer 1

Manipulate is exactly what you are looking for, rather than re-constructing this functionality by hand using Dynamic, which is often more challenging to use:

Manipulate[
 Plot[
   A*100*(Exp[α*100*ϵ] - 1)/(1 + Exp[(β + 1)*α*100*ϵ]),
   {ϵ, 0, 1},
   PlotRange -> All
 ],
 {A, 0, 100}, {α, 0, 100}, {β, 0, 1}
]

Manipulate is very powerful and flexible, and well-worth getting acquainted with: as you look into its documentation, you will also find examples to set the initial values of the parameters, to label them, and much more.