# Chapter 4 - Test - Page 194: 12

$y = 3~csc~\pi x$ The asymptotes have the form $x = n$, for any integer $n$. The period is $2$. We can see the graph below.

#### Work Step by Step

$y = 3~csc~\pi x$ When $x = -1$, then $y = 3~csc~(-\pi)~~$ (which is undefined) When $x = -\frac{1}{2}$, then $y = 3~csc~(-\frac{\pi}{2}) = -3$ When $x = 0$, then $y = 3~csc~0$ (which is undefined) When $x = \frac{1}{2}$, then $y = 3~csc~\frac{\pi}{2} = 3$ When $x = 1$, then $y = 3~csc~\pi~~$ (which is undefined) The asymptotes have the form $x = n$, for any integer $n$. The period is $2$. We can see the graph below.

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