#### Topic: Parameterisation to create family of curves

I'd like to create families of curves, eg f(x)=acos((1+b^2- (x+sqrt(1+b^2))^2)/2*b), each curve defined by a value of 'b'.

Right now it seems I have to duplicate each curve and edit each function, making sure I don't miss any 'b's. This can be tedious. Could there be a 'family' function, where we define range and intervals for 'b'?