Question

find the domain and range of the function ( y = 3sin(x) ). complete the sentence. the functions domain is and the range is.

Explanation:

Step1: Determine the domain of \(y = 3\sin(x)\)

The sine function \(y=\sin(x)\) has no restrictions on the input \(x\). For any real - valued \(x\), the function \(y = 3\sin(x)\) is defined. So the domain of \(y = 3\sin(x)\) is all real numbers, which can be written in interval notation as \((-\infty,\infty)\)

Step2: Determine the range of \(y = 3\sin(x)\)

We know that the range of the basic sine function \(y = \sin(x)\) is \([- 1,1]\), i.e., \(-1\leqslant\sin(x)\leqslant1\).
Multiply each part of the inequality \(-1\leqslant\sin(x)\leqslant1\) by \(3\):

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Answer:

The function's domain is \((-\infty,\infty)\) and the range is \([-3,3]\)