<p>The graph of \(y = x^n\), where&nbsp;\(n \in \mathbb{Z}^-\) , has vertical asymptote given by \(x = 0\).</p>
<p>Case 1: \(n &lt; 0\) and even.<br><br>The graph of \( y = x^{n} \) typically looks like this: </p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1780552157153-24wxg0a91uh.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODA1NTIxNTcxNTMtMjR3eGcwYTkxdWgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2ODE2MSwiZXhwIjoxNzkzNTY4NDYxfQ.MuRCbYDTxd6qKVu0arFHx1Vv9jnknn4j_uufJAii29Q" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Case 2.  \(n &lt; 0\) and odd.<br><br>The graph of \(y = x^n\) typically looks like:</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1780552343063-qj8f25uc4ja.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODA1NTIzNDMwNjMtcWo4ZjI1dWM0amEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2ODE2MSwiZXhwIjoxNzkzNTY4NDYxfQ.e0rC6Du5G1WboiLu4nBdpEKPagKOiXDHnyNlGhs6pLI" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

The graph of \(y = x^n\), where \(n \in \mathbb{Z}^-\) , has vertical asymptote given by \(x = 0\).

Case 1: \(n < 0\) and even.

The graph of \( y = x^{n} \) typically looks like this: 

Power function (negative integral powers)

Power function (negative integral powers)