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<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" xmlns:m="http://www.w3.org/1998/Math/MathML" id="new">
  <name>Interesting Graphs!!!</name>
  <metadata>
  <md:version>1.1</md:version>
  <md:created>2006/04/24 01:07:34.490 GMT-5</md:created>
  <md:revised>2006/04/27 00:15:05.681 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="pradnyab89">
      <md:firstname>Pradnya</md:firstname>
      <md:othername>Vinay</md:othername>
      <md:surname>Bhawalkar</md:surname>
      <md:email>pradnyab89@gmail.com</md:email>
    </md:author>
      <md:author id="kjohnston">
      <md:firstname>Kim </md:firstname>
      <md:othername>Dodge</md:othername>
      <md:surname>Johnston</md:surname>
      <md:email>kim.johnston@fortbend.k12.tx.us</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="pradnyab89">
      <md:firstname>Pradnya</md:firstname>
      <md:othername>Vinay</md:othername>
      <md:surname>Bhawalkar</md:surname>
      <md:email>pradnyab89@gmail.com</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>Graph</md:keyword>
    <md:keyword>Interesting</md:keyword>
    <md:keyword>Rational</md:keyword>
  </md:keywordlist>

  <md:abstract>Graphing graphs that are rational functions, but are a bit different</md:abstract>
</metadata>
  <content>
    <para id="element-352">Although it is always useful to calculate all the good stuff - domain, vertical asymptotes, horizontal asymptotes, slant asymptotes, holes, x- and y-intercepts, there are some graphs that are just different. This lesson is to show you some unique, yet useful graphs. Try graphing them first on the paper provided and then check your answers. The best way to find the pattern that these graphs follow is to plug in points.</para><para id="element-196">Use <link src="http://www.incompetech.com/beta/plainGraphPaper/graph.pdf">graph paper</link>. 
	</para><exercise id="element-189"><problem>
		<para id="element-676">
			<m:math>
<m:apply><m:eq/>
	<m:ci>y</m:ci>
	<m:apply><m:divide/>
		<m:apply><m:abs/><m:ci>x</m:ci></m:apply>
		<m:ci>x</m:ci>
	</m:apply>
</m:apply>
	</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-121"><media type="image/png" src="Interesting1.png"/></figure>
	</solution>
</exercise><exercise id="element-619"><problem>
		<para id="element-773">
			<m:math>
<m:apply><m:eq/>
	<m:ci>y</m:ci>
	<m:apply><m:divide/>
		<m:apply><m:abs/>
			<m:apply><m:minus/>
				<m:ci>x</m:ci>
				<m:cn>2</m:cn>
			</m:apply>
		</m:apply>
		<m:apply><m:minus/>
			<m:ci>x</m:ci>
			<m:cn>2</m:cn>
		</m:apply>
	</m:apply>
</m:apply>
</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-583"><media type="image/png" src="Interesting2.png"/></figure>
	</solution>
</exercise><exercise id="element-461"><problem>
		<para id="element-828"><m:math><m:apply><m:eq/>
<m:ci>y</m:ci>

<m:apply><m:divide/>
	<m:apply><m:abs/>
		<m:apply><m:plus/>
			<m:ci>x</m:ci>
			<m:cn>3</m:cn>
		</m:apply>
	</m:apply>
	<m:apply><m:plus/>
		<m:ci>x</m:ci>
		<m:cn>3</m:cn>
	</m:apply>
</m:apply>
</m:apply>
</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-657"><media type="image/png" src="Interesting3.png"/></figure>
	</solution>
</exercise><exercise id="element-172"><problem>
		<para id="element-374">
			<m:math>
<m:apply><m:eq/>
	<m:ci>y</m:ci>
	<m:apply><m:divide/>
		<m:apply><m:abs/>
			<m:apply><m:plus/>
				<m:ci>x</m:ci>
				<m:cn>2</m:cn>
			</m:apply>
		</m:apply>
		<m:ci>x</m:ci>
	</m:apply>
</m:apply>
</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-622"><media type="image/png" src="Interesting4.png"/></figure>
	</solution>
</exercise><exercise id="element-936"><problem>
		<para id="element-938">
			<m:math>
<m:apply><m:eq/>
	<m:ci>y</m:ci>
	<m:apply><m:divide/>
		<m:ci>x</m:ci>
		<m:apply><m:root/>
			<m:apply><m:power/>
				<m:ci>x</m:ci>
				<m:cn>2</m:cn>
			</m:apply>
		</m:apply>
	</m:apply>
</m:apply>
</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-76"><media type="image/png" src="Interesting5.png"/></figure>
	</solution>
</exercise><exercise id="element-566"><problem>
		<para id="element-15">
			<m:math>
<m:apply><m:eq/>
	<m:ci>y</m:ci>
	<m:apply><m:divide/>
		<m:ci>x</m:ci>
		<m:apply><m:root/>
			<m:apply><m:plus/>
				<m:apply><m:power/>
					<m:ci>x</m:ci>
					<m:cn>2</m:cn>
				</m:apply>
				<m:cn>2</m:cn>
			</m:apply>
		</m:apply>
	</m:apply>
</m:apply>
</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-106"><media type="image/png" src="Interesting6.png"/></figure>
	</solution>
</exercise><exercise id="element-981"><problem>
		<para id="element-120">
			<m:math>
<m:apply><m:eq/>
	<m:ci>y</m:ci>
	<m:apply><m:divide/>
		<m:apply><m:times/>
			<m:cn>-6</m:cn>
			<m:ci>x</m:ci>
		</m:apply>
		<m:apply><m:root/>
			<m:apply><m:plus/>
				<m:apply><m:times/>
					<m:cn>4</m:cn>
					<m:apply><m:power/>
						<m:ci>x</m:ci>
						<m:cn>2</m:cn>
					</m:apply>
				</m:apply>
				<m:cn>5</m:cn>
			</m:apply>
		</m:apply>
	</m:apply>
</m:apply>
</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-652"><media type="image/png" src="Interesting7.png"/></figure>
	</solution>
</exercise><exercise id="element-562"><problem>
		<para id="element-896">
			<m:math>
<m:apply><m:eq/>
	<m:ci>y</m:ci>
	<m:apply><m:divide/>
		<m:apply><m:times/>
			<m:cn>2</m:cn>
			<m:ci>x</m:ci>
		</m:apply>
		<m:apply><m:root/>
			<m:apply><m:plus/>
				<m:apply><m:power/>
					<m:ci>x</m:ci>
					<m:cn>2</m:cn>
				</m:apply>
				<m:cn>5</m:cn>
			</m:apply>
		</m:apply>
	</m:apply>
</m:apply>
</m:math>
		</para>
	</problem>

	<solution>
		<figure id="element-710"><media type="image/png" src="Interesting8.png"/></figure>
	</solution>
</exercise>   
  </content>
  
</document>
