Identify the amplitude and period of \( g(x)=3 \sin 2 x \). Then identify the graph of the function and describe the graph of \( g \) as a transformation of the graph of its parent functi) The amplitude is \( 3 \checkmark \) and the period is \( \square \).

The period of the function \( g(x) = 3 \sin 2x \) can be determined using the formula \( \frac{2\pi}{|B|} \), where \( B \) is the coefficient of \( x \). Here, \( B = 2 \), so the period is \( \frac{2\pi}{2} = \pi \). When it comes to the graph, \( g(x) \) is a vertical stretch of the parent function \( \sin x \) by a factor of 3, making it reach a maximum of 3 and a minimum of -3. Additionally, the graph compresses horizontally due to the factor of 2, resulting in cycles that complete faster—in this case, they repeat every \( \pi \) units instead of \( 2\pi \). Thus, you see steeper waves that oscillate between 3 and -3!