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…

Explanation:

Step1: Recall range of sin(x)

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

Step2: Multiply by - 3

When we multiply the inequality (-1\leqslant\sin(x)\leqslant1) by (-3), the direction of the inequality signs changes. So we get (3\geqslant - 3\sin(x)\geqslant - 3) (since multiplying by a negative number reverses the inequality).

Step3: Subtract 4

Subtract 4 from each part of the inequality (3\geqslant - 3\sin(x)\geqslant - 3). We have (3 - 4\geqslant-3\sin(x)-4\geqslant - 3 - 4), which simplifies to (-1\geqslant y\geqslant - 7) or (-7\leqslant y\leqslant - 1).

Answer:

all real numbers (-7\leqslant y\leqslant - 1)