Let f(x) a sin (k(r - d)) +c, for 1 < x<7. The graph of f is shown on the diagram below. A 5.+ 4 3 21 1 1. 2 3 4 The graph of f has a maximum at A(2, 5) and a minimum at B(4, 1). (a) Find the value of: (i). a; (ii) c. (b) (i) Find the value of k. (ii) Find the smallest possible value of d, given d> 0. () The graph of f is translated by a vector to give the graph of a function g such that x) =3 has only one solution in the given domain. (c) Find the value of b.

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