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The domain of f(x)=3sin(2x) is all real numbers

----Any number can be input into this function and receive a valid output

The range of f(x)=3sin(2x) is [-3,3]

----The range of y=sin(x) is [-1,1] frequency modulation, which happens when the argument of a sine function is modified, does not affect the range of a cosine or sine function, so the range of y=sin(2x) is also [-1,1]. Amplitude modulation, which happens when the entire function is multiplied by a numerical constant, does affect the range. If any number put into y=sin(2x) will output a maximum of 1, the most an input can cause in y=3sin(2x) will be 3 times the maximum of y=sin(2x), and the same for the minimums, so the range of y=3sin(2x) is from -3 to 3.

If you would like a more complete explanation of the concepts underlying domain and range of functions, message me and I can more completely explain them.

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Q: What is the domain and range for the function 3sin2x?
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