<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 640px;"><colgroup><col style="width: 120px;"><col style="width: 150px;"><col style="width: 150px;"><col style="width: 220px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$y=a{{x}^{n}}$</th><th style="text-align: center; --cell-justify: center">$a&gt;0$</th><th style="text-align: center; --cell-justify: center">$a&lt;0$</th><th style="text-align: center; --cell-justify: center">Notes</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center; vertical-align: top">For $n=0$,$y=a$</td><td style="text-align: center; --cell-justify: center; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765901684720-2fystm9nrsb.png"></td><td style="text-align: center; --cell-justify: center; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765901706211-tfsmyk27av.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><ul><li>It is a horizontal line since ${{x}^{0}}=1$.</li></ul></td></tr><tr><td style="text-align: center; --cell-justify: center; vertical-align: top">For $n=1$, $y=ax$</td><td style="text-align: center; --cell-justify: center; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902396493-qxu9cl9sckc.png"></td><td style="text-align: center; --cell-justify: center; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902421518-60c19tkxm46.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><ul><li>It is a straight line graph, either sloping upwards or sloping downwards depending on its gradient which is the value of $a$.</li></ul></td></tr><tr><td style="text-align: center; --cell-justify: center; vertical-align: top">For $n=2$, $y=a{{x}^{2}}$</td><td style="text-align: center; --cell-justify: center; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902444316-y0k7ome9x0s.png"></td><td style="text-align: center; --cell-justify: center; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902463622-l8wagj8xhpn.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><ul><li>It is a quadratic graph, either opening upwards or downwards depending on the value of $a$.</li></ul></td></tr><tr><td style="text-align: left; --cell-justify: flex-start; vertical-align: top">For $n=3$, $y=a{{x}^{3}}$</td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902493112-kbv9vteh6e.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902514474-vor7z8f2jv.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><ul><li>It is a cubic graph.</li></ul></td></tr><tr><td style="text-align: left; --cell-justify: flex-start; vertical-align: top">For ${n = -1}$, ${y = ax^{-1}}$ ${= \frac{a}{x}}$</td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902552545-aasz1hif3vc.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902590882-lscr33imnw.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><ul><li>It is a reciprocal graph.</li><li>The graph occurs in two separate parts but it is considered as a single graph.</li><li>When $x=0$, the function $y=\frac{a}{x}$ is not defined. This means that there is a break at $x=0$.</li><li>The graph approach very close to both the $x$-axis and $y$-axis but never meet them. The axes are known as asymptotes.</li></ul></td></tr><tr><td style="text-align: left; --cell-justify: flex-start; vertical-align: top">For ${n = -2}$, ${y = ax^{-2}}$ ${= \frac{a}{x^2}}$</td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902636764-hktkqxy37y.png"></td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765902654942-5nqs90vod5d.png"> </td><td style="text-align: left; --cell-justify: flex-start; vertical-align: top"><ul><li>It is a reciprocal graph.</li><li>The graph occurs in two separate parts but it is considered as a single graph.</li><li>When $x=0$, the function $y=\frac{a}{{{x}^{2}}}$ is not defined. This means that there is a break at $x=0$.</li><li>The graph approach very close to both the $x$-axis and $y$-axis but never meet them. The axes are known as asymptotes.</li><li>Since ${{x}^{2}}&gt;0$, hencewhen $a&gt;0$, the graph will on the positive $y$-axis andwhen $a&lt;0$, the graph will on the negative $y$-axis</li></ul></td></tr></tbody></table></div></div>

<ul><li>It is a horizontal line since ${{x}^{0}}=1$.</li></ul>

<ul><li>It is a straight line graph, either sloping upwards or sloping downwards depending on its gradient which is the value of $a$.</li></ul>

<ul><li>It is a quadratic graph, either opening upwards or downwards depending on the value of $a$.</li></ul>

<ul><li>It is a cubic graph.</li></ul>

For ${n = -1}$, ${y = ax^{-1}}$ ${= \frac{a}{x}}$

<ul><li>It is a reciprocal graph.</li><li>The graph occurs in two separate parts but it is considered as a single graph.</li><li>When $x=0$, the function $y=\frac{a}{x}$ is not defined. This means that there is a break at $x=0$.</li><li>The graph approach very close to both the $x$-axis and $y$-axis but never meet them. The axes are known as asymptotes.</li></ul>

For ${n = -2}$, ${y = ax^{-2}}$ ${= \frac{a}{x^2}}$

<ul><li>It is a reciprocal graph.</li><li>The graph occurs in two separate parts but it is considered as a single graph.</li><li>When $x=0$, the function $y=\frac{a}{{{x}^{2}}}$ is not defined. This means that there is a break at $x=0$.</li><li>The graph approach very close to both the $x$-axis and $y$-axis but never meet them. The axes are known as asymptotes.</li><li>Since ${{x}^{2}}&gt;0$, hencewhen $a&gt;0$, the graph will on the positive $y$-axis andwhen $a&lt;0$, the graph will on the negative $y$-axis</li></ul>

Graphs of Power Functions $y=a{{x}^{n}}$, where $n=3,2,1,0,-1$ and $-2$

Graphs of Power Functions $y=a{{x}^{n}}$, where $n=3,2,1,0,-1$ and $-2$

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