what is the range of y = -3sin(x) - 4?\no all real numbers -7≤y≤7\no all real numbers -7≤y≤-1\no all real…

Explanation:

Step1: Recall sine - function range

The range of the basic sine function $y = \sin(x)$ is $- 1\leqslant\sin(x)\leqslant1$.

Step2: Multiply by - 3

When we multiply $\sin(x)$ by $-3$, the inequality signs reverse. So, $-3\times1\leqslant - 3\sin(x)\leqslant-3\times(-1)$, which simplifies to $-3\leqslant - 3\sin(x)\leqslant3$.

Step3: Subtract 4

Subtract 4 from each part of the inequality: $-3 - 4\leqslant-3\sin(x)-4\leqslant3 - 4$. This gives $-7\leqslant y\leqslant - 1$.

Answer:

all real numbers $-7\leqslant y\leqslant - 1$