\( 16 \quad \begin{array}{l}\text { Determine the amplitude, period, and phase shift of the } \\ \text { function. Graph the function. } \\ y=4 \cos (3 x+\pi) \\ \text { The amplitude is } 4 \text {. } \\ \text { (Simplity your answer.) } \\ \text { The period is } \\ \text { (Type an exact answer, using } \pi \text { as needed. Use integers or } \\ \text { fractions for any numbers in the expression.) }\end{array} \)

The period of a cosine function is determined by the coefficient of \( x \) in the equation. For the function \( y = 4 \cos(3x + \pi) \), the period is calculated using the formula \( \frac{2\pi}{|B|} \), where \( B \) is the coefficient of \( x \). In this case, \( B = 3 \), so the period is \( \frac{2\pi}{3} \). The phase shift is found by setting the inside of the cosine function equal to zero: \( 3x + \pi = 0 \). Solving for \( x \) gives a phase shift of \( -\frac{\pi}{3} \) to the left. So, the amplitude is 4, the period is \( \frac{2\pi}{3} \), and the phase shift is \( -\frac{\pi}{3} \). Happy graphing!