what is the range of y = -3sin(x) - 4? all real numbers -7≤y≤7 all real numbers -7≤y≤-1 all real numbers…

Explanation:

Step1: Recall range of basic sine function

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

Step2: Multiply by -3

When we multiply the inequality by -3, the direction of the inequality signs changes. 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 all parts of the inequality: $-3 - 4\leqslant-3\sin(x)-4\leqslant3 - 4$. This gives $-7\leqslant y\leqslant - 1$.

Answer:

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