\( 1 \leftarrow \quad \begin{array}{l}\text { Determine the amplitude and period of the function. Graph } \\ \text { the function. } \\ y=-\frac{1}{2} \cos \frac{\pi}{2} x \\ \text { The amplitude is } \square . \\ \text { (Simplify your answer.) }\end{array} \)

The amplitude of the function \( y = -\frac{1}{2} \cos \frac{\pi}{2} x \) is the absolute value of the coefficient in front of the cosine function. Since the coefficient is \(-\frac{1}{2}\), the amplitude is \( \left| -\frac{1}{2} \right| = \frac{1}{2} \). The period of the function can be determined using the formula \( \frac{2\pi}{b} \), where \( b \) is the coefficient of \( x \) inside the cosine function. In this case, \( b = \frac{\pi}{2} \), so the period is \( \frac{2\pi}{\frac{\pi}{2}} = 4 \). To graph the function, you would plot the key points: start at \( (0, -\frac{1}{2}) \), peak at \( (1, \frac{1}{2}) \), go down to \( (2, -\frac{1}{2}) \), reach a trough at \( (3, -\frac{1}{2}) \), and return to \( (4, \frac{1}{2}) \). Repeat this pattern to the left and right to continue the graph! The amplitude is \( \frac{1}{2} \).