# Chapter 4 - Test - Page 647: 17

See graph and explanations.

#### Work Step by Step

Step 1. Given the function $y=-\frac{1}{2}csc(\pi x)$, we can identify its period as $p=\frac{2\pi}{\pi}=2$ Step 2. To graph the function, start from $y=sin(x)$, shrink horizontally by a factor of $\pi$ to get $y=sin(\pi x)$ (green curve), use the reciprocal property to get $y=csc(\pi x)$ (blue curve), shrink vertically by a factor of 2 and reflect around the x-axis to get the red curve of $y=-\frac{1}{2}csc(\pi x)$.

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