Question

Find the range of the function $y=\sin 3x+3$.

Answer 1

Given the function, $y=\sin 3x+3$ can be written as,

$\sin 3x=y-3$.

As we know,

$-1\le \sin 3x\le 1$ $\forall x\in R$

or, $-1\le y-3\le 1$

or, $2\le y\le 4$.

So range of $y$ is $[2,4]$.