If the function y is equal to sine x is transformed to y is equal to 3 sine open paren 2 thirds x close paren , how do the amplitude and period change?

For y = 3 sin((2/3)x), the amplitude is the absolute value of the coefficient outside sine, so it changes from 1 to 3 and increases. The period is 2π divided by the coefficient of x: 2π ÷ (2/3) = 3π, which is longer than the original period of 2π. Therefore, the amplitude and period both increase; the correct choice is D, “The amplitude increases, and the period increases.”

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