Determine the amplitude of the function \( y=4 \boldsymbol{\operatorname { s i n }} x \). Graph the function and \( y=\sin x \). The amplitude is \( \square \). (Simplify your answer.)

The amplitude of the function \( y = 4 \sin x \) is simply the coefficient in front of the sine function, which is 4. This means the graph of \( y = 4 \sin x \) will oscillate between 4 and -4, showing a much taller wave compared to the standard \( y = \sin x \), which oscillates between 1 and -1. To visualize this, when you graph both functions, you'll notice that \( y = 4 \sin x \) reaches higher peaks and lower troughs than the standard sine function. This amplifies the wave effect, making it appear more pronounced and dynamic! So, the amplitude is \( 4 \).