Answer:
The range of the function is [-7,-1].
Step-by-step explanation:
The given function is
[tex]y=-3\sin (x)-4[/tex]
We know that the range of sine function is [-1,1].
[tex]-1\leq \sin (x)\leq 1[/tex]
Multiply all sides by -3.
[tex]3\geq -3\sin (x)\geq -3[/tex]
Subtract 4 form each side.
[tex]3-4\geq -3\sin (x)-4\geq -3-4[/tex]
[tex]-1\geq y\geq -7[/tex]
The value of y lie from -7 to -1.
Therefore the range of the function is [-7,-1].
