Trig Function

the function g(x) is c+d sinx the range of g is given by -4<g(x)<10
find values of constant c and d.i know max value of sinx graph is 1 and min is -1 so if i substitute in for x i get the answer but just wanted to know isn't the max and min 1 and -1 only when no change is made to sinx graph because here the graph has been transformed right, so max and min are no more at 1 and -1. can someone clear this out for me.

You are right, max and min of +1 and -1 occur when you are only dealing with $\sin x$ on its own.

But it's not difficult to obtain max and min for the transformed graph;

$-1 \leq \sin x \leq 1$

Multiply through by $d$;

$-d \leq d \sin x \leq d$

Add $c$ to everything;

$c-d \leq c+d\sin x \leq c+d$


So the min and max values are precisely just $c-d$ and $c+d$ repsectively.