1. The point $P(3,2)$ lies on the curve with equation $y=f(x).$

(i) On the graph of $y=f(x)+a$, where $a$is a constant, the point $P$ is mapped to the point $(3,-5)$.  Determine the value of  $a$.

(ii) On the graph of $y=f(x+b)$, where $b$is a constant, the point $P$ is mapped to the point $(-1,2).$  Determine the value of $b$.

(iii) On the graph of $y=cf(x),$, where $c$is a constant, the point $P$is mapped to the point $(3,1)$.  Determine the value of $c$.

(iv) On the graph of $y=f(dx),$, where $d$is a constant, the point $P$ is mapped to the point $(1,2)$.  Determine the value of $d$.