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You need to find the domain of the function `y = 3sin 2x` , hence, `x in R` .
You need to find the range of function, such that:
`-1*3 <= 3sin2x <= 1*3 => -3 <= 3sin 2x <= 3 => y in [-3,3]`
You need to find the amplitude, hence `a = 3` .
There is no phase shift and since the function is horizontally stretched by 2 yields that you may evaluate the period such that:
`T = (2pi)/2 => T = pi`
Hence, evaluating the domain of the function yields `x in R` , the range of the function is `y in [-3,3]` , the amplitude of the function is `a = 3` , the period of the function is `T = pi` and there is no phase shift.
Sketching th graph, yields:
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