Investigate the family of functions f(x) = in (sin x + C). What features fo the members

Question:

Investigate the family of functions f(x) = in (sin x + C). What features fo the members of this family have in common? How do they differ? For which values of C is f continuous on (– ∞, ∞)? For which values of C does f have no graph at all? What happens as C → ∞?