Polynomial Functions: Overview of Polynomial Functions - Unit One</t= itle> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceType"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceName"/>  <style>  </style>  </head> <body lang=3DEN-US link=3Dblue vlink=3Dpurple style=3D'tab-interval:.5in'> <div class=3DSection1> Overview of <a href=3D"http://en.wikipedia.org/wiki/Pol= ynomial">Polynomial</a> <a href=3D"http://en.wikipedia.org/wiki/Function_%28mathematics%29">Functio= ns</a>: Definition, Examples, Illustrations, Characteristics <o:p> </o:p> ***********= *********************************<o:p></o:p> <o:p> </o:p> Definition: A singl= e input variable with real coefficients and non-negative integer exponents = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; which is set equal to a single outp= ut variable. <o:p> </o:p> Examples: &n= bsp; y =3D 3x +4 &nbs= p; y =3D x2 – x + 6 = y =3D 2x3 += 4x2 – x + 5 y = =3D x4–x3+2x2–x+3 etc̷= 0; <o:p> </o:p> <= !--[if gte vml 1]><v:group id=3D"_x0000_s1105" style=3D'position:absolute;left:0;text-align:left; margin-left:254.65pt;margin-top:14.5pt;width:15.55pt;height:17.65pt;z-inde= x:15' coordorigin=3D"10189,1607" coordsize=3D"311,353"> <v:line id=3D"_x0000_s1106" style=3D'position:absolute;flip:x' from=3D"103= 56,1607" to=3D"10358,1960" strokeweight=3D"2.25pt"/> <v:line id=3D"_x0000_s1107" style=3D'position:absolute;rotation:90;flip:x'= from=3D"10337,1639" to=3D"10353,1950" strokeweight=3D"2.25pt"/> </v:group><![endif]--><![if !vml]><img width=3D24 height=3D28 src=3D"PolynomialFunctionsUnitOneAOV_files/image001.gif" v:shapes=3D"_x0000= _s1105 _x0000_s1106 _x0000_s1107"><![endif]><![if !vml]><img width=3D145 height=3D90 src=3D"PolynomialFunctionsUnitOneAOV_files/image004.gif" v:shapes=3D"_x0000= _s1097"><![endif]><![if !vml]><img width=3D121 height=3D95 src=3D"PolynomialFunctionsUnitOneAOV_files/image005.gif" v:shapes=3D"_x0000= _s1055"><![endif]><![if !vml]><img width=3D96 height=3D98 src=3D"PolynomialFunctionsUnitOneAOV_files/image006.gif" v:shapes=3D"_x0000= _s1095"><![endif]>Illustrations: &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; <![if !vml]><img width=3D25 height=3D28 src=3D"PolynomialFunctionsUnitOneAOV_files/image002.gif" v:shapes=3D"_x0000= _s1102 _x0000_s1103 _x0000_s1104"><![endif]><![if !vml]><img width=3D101 height=3D81 src=3D"PolynomialFunctionsUnitOneAOV_files/image008.gif" v:shapes=3D"_x0000= _s1026"><![endif]><![if !vml]><img width=3D25 height=3D27 src=3D"PolynomialFunctionsUnitOneAOV_files/image003.gif" v:shapes=3D"_x0000= _s1099 _x0000_s1100 _x0000_s1101"><![endif]> &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; = <![if !vml]><img width=3D24 height=3D28 src=3D"PolynomialFunctionsUnitOneAOV_files/image001.gif" v:shapes=3D"_x0000= _s1060 _x0000_s1061 _x0000_s1062"><![endif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; &= nbsp; &nbs= p; etc… Characteristics: = ; <o:p></o:p> = ; <o:p></o:p> = ; Infinite Set of Points (Arrows) = ; &n= bsp; Infinite Set of Positive (+) Curves or S= olution Sets<o:p></o:p> <o:p> </o:p> </= span>Up and To Right (+) Orientation &= nbsp; </s= pan>(X) Intercepts: Highest Degree =3D # of (X) Intercepts &nbs= p; <o:p> </o:p> Maximums & Minimums Points: Bumps =3D> (Relatives) or = Arrows =3D> (Absolutes)<o:p>= </o:p> <o:p> </o:p> <o:p> </o:p> ***********= ********************************* &nbs= p; &= nbsp; Definition: A singl= e input variable with real coefficients and non-negative integer exponents = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; which is set equal to a single output variable. <o:p> </o:p> Examples: &n= bsp; y =3D – 3x +4 &n= bsp; y =3D – x2 – x + 6 y =3D – 2x3= + 4x2 – x + 5 y =3D –x<s= up>4+x3–2x2+x–3 etc… <o:p> </o:p> <![if !vml]><img width=3D81 height=3D85 src=3D"PolynomialFunctionsUnitOneAOV_files/image010.gif" v:shapes=3D"_x0000= _s1030"><![endif]><![if !vml]><img width=3D86 height=3D86 src=3D"PolynomialFunctionsUnitOneAOV_files/image011.gif" v:shapes=3D"_x0000= _s1091"><![endif]><![if !vml]><img width=3D145 height=3D90 src=3D"PolynomialFunctionsUnitOneAOV_files/image007.gif" v:shapes=3D"_x0000= _s1080 _x0000_s1075 _x0000_s1076"><![endif]><![if !vml]><img width=3D128 height=3D76 src=3D"PolynomialFunctionsUnitOneAOV_files/image013.gif" v:shapes=3D"_x0000= _s1052"><![endif]>Illustrations: <![if !vml]><img width=3D28 height=3D4 src=3D"PolynomialFunctionsUnitOneAOV_files/image014.gif" v:shapes=3D"_x0000= _s1094"><![endif]> = &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; = <![if !vml]><img width=3D28 height=3D4 src=3D"PolynomialFunctionsUnitOneAOV_files/image014.gif" v:shape= s=3D"_x0000_s1093"><![endif]><![if !vml]><img width=3D28 height=3D4 src=3D"PolynomialFunctionsUnitOneAOV_files/image014.gif" v:shapes=3D"_x0000= _s1077"><![endif]> &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; = &= nbsp; &= nbsp; &nbs= p; etc&#= 8230; = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; </spa= n> Characteristics: &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; = </= span> &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; </= span>Infinite Set of Points (Arrows) = ; &n= bsp; Infinite Set of Negative (–) Curves= or Solution Sets<o:p></o:p> <o:p> </o:p> </= span>Down and To Left= (–) Orientation </= span>(X) Intercepts: Highest Degree =3D # of (X) Intercepts = <o:p></o:p> <o:p> </o:p> = ; Maximums & Minimums Points: Bumps =3D> (Relatives) or Arrows =3D> (Absolutes) <o:p> </o:p> ***********= ********************************* The total set</spa= n> of Polynomial Functions consists of all the Positive and Negative equatio= ns and curves represented in the two gro= ups above. Viewing Polynomials <b= >as a total allows for a better understanding of the solution set that is generated from these mysterious equations (functions x,y). Students should be expected to demonstrate= their conceptual knowledge of Polynomials by creating sets of Ps &Ns. <o:p> </o:p> Below is a more formal Mathematical Definition: A <a href=3D"http://en.wikipedia.org/wiki/Polynomial">polynomial</a> <a href=3D"http://en.wikipedia.org/wiki/Function_%28mathematics%29">function</= a> of degree n is a function def= ined by an equation of the form: f(x) =3Danxn + an-1<= /sub>xn-1+… a1x + a0 where (1) an, an-1, .., a1= , a0 are real numbers, (2) an does not equal to 0, and <!FONT SIZE=3D-1>(3)<!/FONT> = n is an integer greater or equal to 0</>. The domain is (̵= 1;∞,+∞). The range is (–∞= ,+∞). If a>0 then PF leans to right &= amp; if a<0 then leans to left & a<>0! <o:p> </o:p> <o:p> </o:p> Tom Love = &nb= sp; <st1:place w:st=3D"on"><st1:PlaceName w:st=3D"on">Malone</st1:PlaceN= ame> <st1:PlaceType w:st=3D"on">College</st1:PlaceType></st1:place> = &nb= sp; Fall 2007<o:p></o:p> <o:p> </o:p> <o:p> </o:p> <o:p>&nb= sp;</o:p> </div> </body> </html> ------=_NextPart_01C8194E.037A7680 Content-Location: file:///C:/A5138E36/PolynomialFunctionsUnitOneAOV_files/image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAU ABgAgAAAAAAAAAIzhH+hyG0anHxrOmhvzQjzvn2AJ47hR4opCLVr4sbyTLdTHUlvtlv9feL8dEFe 0XcE5hoFADs= ------=_NextPart_01C8194E.037A7680 Content-Location: file:///C:/A5138E36/PolynomialFunctionsUnitOneAOV_files/image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAV 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align=3Dleft size=3D1> <![endif]> </div> <div style=3D'mso-element:endnote-separator' id=3Des> <![if !supportFootnotes]> <hr align=3Dleft size=3D1 width=3D"33%"> <![endif]> </div> <div style=3D'mso-element:endnote-continuation-separator' id=3Decs> <![if !supportFootnotes]> <hr align=3Dleft size=3D1> <![endif]> </div> <div style=3D'mso-element:footer' id=3Df1> Tom Love= = &nb= sp; <st1:place w:st=3D"on"><st1:PlaceName w:st=3D"on">Malone</st1:PlaceN= ame> <st1:PlaceType w:st=3D"on">College</st1:PlaceType></st1:place> = &nb= sp; Fall 2003<o:p></o:p> </div> </body> </html> ------=_NextPart_01C8194E.037A7680 Content-Location: file:///C:/A5138E36/PolynomialFunctionsUnitOneAOV_files/image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkQBaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQCH AFIAgAAAAAAAAAL/BGKpy+0Po5y01oCs3rx7mxlY+JXmiSaYOpLpC8dMK9LyjaNttrv5D5TsasOg 8bjoHXo+pPPGXNqe1F+UWM3mlFitFzaarb7kU1jcLKsnZ/T6DRq74fRIOymvT+l3fJp89bbnx8fU 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MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C8194E.037A7680" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C8194E.037A7680 Content-Location: file:///C:/A5138E36/PolynomialFunctionsUnitOneAOV.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Polynomial Functions: Overview of Polynomial Functions - Unit One</t= itle> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceType"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceName"/>  <style>  </style>  </head> <body lang=3DEN-US link=3Dblue vlink=3Dpurple style=3D'tab-interval:.5in'> <div class=3DSection1> Overview of <a href=3D"http://en.wikipedia.org/wiki/Pol= ynomial">Polynomial</a> <a href=3D"http://en.wikipedia.org/wiki/Function_%28mathematics%29">Functio= ns</a>: Definition, Examples, Illustrations, Characteristics <o:p> </o:p> ***********= *********************************<o:p></o:p> <o:p> </o:p> Definition: A singl= e input variable with real coefficients and non-negative integer exponents = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; which is set equal to a single outp= ut variable. <o:p> </o:p> Examples: &n= bsp; y =3D 3x +4 &nbs= p; y =3D x2 – x + 6 = y =3D 2x3 += 4x2 – x + 5 y = =3D x4–x3+2x2–x+3 etc̷= 0; <o:p> </o:p> <= !--[if gte vml 1]><v:group id=3D"_x0000_s1105" style=3D'position:absolute;left:0;text-align:left; margin-left:254.65pt;margin-top:14.5pt;width:15.55pt;height:17.65pt;z-inde= x:15' coordorigin=3D"10189,1607" coordsize=3D"311,353"> <v:line id=3D"_x0000_s1106" style=3D'position:absolute;flip:x' from=3D"103= 56,1607" to=3D"10358,1960" strokeweight=3D"2.25pt"/> <v:line id=3D"_x0000_s1107" style=3D'position:absolute;rotation:90;flip:x'= from=3D"10337,1639" to=3D"10353,1950" strokeweight=3D"2.25pt"/> </v:group><![endif]--><![if !vml]><img width=3D24 height=3D28 src=3D"PolynomialFunctionsUnitOneAOV_files/image001.gif" v:shapes=3D"_x0000= _s1105 _x0000_s1106 _x0000_s1107"><![endif]><![if !vml]><img width=3D145 height=3D90 src=3D"PolynomialFunctionsUnitOneAOV_files/image004.gif" v:shapes=3D"_x0000= _s1097"><![endif]><![if !vml]><img width=3D121 height=3D95 src=3D"PolynomialFunctionsUnitOneAOV_files/image005.gif" v:shapes=3D"_x0000= _s1055"><![endif]><![if !vml]><img width=3D96 height=3D98 src=3D"PolynomialFunctionsUnitOneAOV_files/image006.gif" v:shapes=3D"_x0000= _s1095"><![endif]>Illustrations: &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; <![if !vml]><img width=3D25 height=3D28 src=3D"PolynomialFunctionsUnitOneAOV_files/image002.gif" v:shapes=3D"_x0000= _s1102 _x0000_s1103 _x0000_s1104"><![endif]><![if !vml]><img width=3D101 height=3D81 src=3D"PolynomialFunctionsUnitOneAOV_files/image008.gif" v:shapes=3D"_x0000= _s1026"><![endif]><![if !vml]><img width=3D25 height=3D27 src=3D"PolynomialFunctionsUnitOneAOV_files/image003.gif" v:shapes=3D"_x0000= _s1099 _x0000_s1100 _x0000_s1101"><![endif]> &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; = <![if !vml]><img width=3D24 height=3D28 src=3D"PolynomialFunctionsUnitOneAOV_files/image001.gif" v:shapes=3D"_x0000= _s1060 _x0000_s1061 _x0000_s1062"><![endif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; &= nbsp; &nbs= p; etc… Characteristics: = ; <o:p></o:p> = ; <o:p></o:p> = ; Infinite Set of Points (Arrows) = ; &n= bsp; Infinite Set of Positive (+) Curves or S= olution Sets<o:p></o:p> <o:p> </o:p> </= span>Up and To Right (+) Orientation &= nbsp; </s= pan>(X) Intercepts: Highest Degree =3D # of (X) Intercepts &nbs= p; <o:p> </o:p> Maximums & Minimums Points: Bumps =3D> (Relatives) or = Arrows =3D> (Absolutes)<o:p>= </o:p> <o:p> </o:p> <o:p> </o:p> ***********= ********************************* &nbs= p; &= nbsp; Definition: A singl= e input variable with real coefficients and non-negative integer exponents = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; which is set equal to a single output variable. <o:p> </o:p> Examples: &n= bsp; y =3D – 3x +4 &n= bsp; y =3D – x2 – x + 6 y =3D – 2x3= + 4x2 – x + 5 y =3D –x<s= up>4+x3–2x2+x–3 etc… <o:p> </o:p> <![if !vml]><img width=3D81 height=3D85 src=3D"PolynomialFunctionsUnitOneAOV_files/image010.gif" v:shapes=3D"_x0000= _s1030"><![endif]><![if !vml]><img width=3D86 height=3D86 src=3D"PolynomialFunctionsUnitOneAOV_files/image011.gif" v:shapes=3D"_x0000= _s1091"><![endif]><![if !vml]><img width=3D145 height=3D90 src=3D"PolynomialFunctionsUnitOneAOV_files/image007.gif" v:shapes=3D"_x0000= _s1080 _x0000_s1075 _x0000_s1076"><![endif]><![if !vml]><img width=3D128 height=3D76 src=3D"PolynomialFunctionsUnitOneAOV_files/image013.gif" v:shapes=3D"_x0000= _s1052"><![endif]>Illustrations: <![if !vml]><img width=3D28 height=3D4 src=3D"PolynomialFunctionsUnitOneAOV_files/image014.gif" v:shapes=3D"_x0000= _s1094"><![endif]> = &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; = <![if !vml]><img width=3D28 height=3D4 src=3D"PolynomialFunctionsUnitOneAOV_files/image014.gif" v:shape= s=3D"_x0000_s1093"><![endif]><![if !vml]><img width=3D28 height=3D4 src=3D"PolynomialFunctionsUnitOneAOV_files/image014.gif" v:shapes=3D"_x0000= _s1077"><![endif]> &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; = &= nbsp; &= nbsp; &nbs= p; etc&#= 8230; = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; </spa= n> Characteristics: &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; = </= span> &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; </= span>Infinite Set of Points (Arrows) = ; &n= bsp; Infinite Set of Negative (–) Curves= or Solution Sets<o:p></o:p> <o:p> </o:p> </= span>Down and To Left= (–) Orientation </= span>(X) Intercepts: Highest Degree =3D # of (X) Intercepts = <o:p></o:p> <o:p> </o:p> = ; Maximums & Minimums Points: Bumps =3D> (Relatives) or Arrows =3D> (Absolutes) <o:p> </o:p> ***********= ********************************* The total set</spa= n> of Polynomial Functions consists of all the Positive and Negative equatio= ns and curves represented in the two gro= ups above. Viewing Polynomials <b= >as a total allows for a better understanding of the solution set that is generated from these mysterious equations (functions x,y). Students should be expected to demonstrate= their conceptual knowledge of Polynomials by creating sets of Ps &Ns. <o:p> </o:p> Below is a more formal Mathematical Definition: A <a href=3D"http://en.wikipedia.org/wiki/Polynomial">polynomial</a> <a href=3D"http://en.wikipedia.org/wiki/Function_%28mathematics%29">function</= a> of degree n is a function def= ined by an equation of the form: f(x) =3Danxn + an-1<= /sub>xn-1+… a1x + a0 where (1) an, an-1, .., a1= , a0 are real numbers, (2) an does not equal to 0, and <!FONT SIZE=3D-1>(3)<!/FONT> = n is an integer greater or equal to 0</>. The domain is (̵= 1;∞,+∞). The range is (–∞= ,+∞). If a>0 then PF leans to right &= amp; if a<0 then leans to left & a<>0! <o:p> </o:p> <o:p> </o:p> Tom Love = &nb= sp; <st1:place w:st=3D"on"><st1:PlaceName w:st=3D"on">Malone</st1:PlaceN= ame> <st1:PlaceType w:st=3D"on">College</st1:PlaceType></st1:place> = &nb= sp; Fall 2007<o:p></o:p> <o:p> </o:p> <o:p> </o:p> <o:p>&nb= sp;</o:p> </div> </body> </html> ------=_NextPart_01C8194E.037A7680 Content-Location: file:///C:/A5138E36/PolynomialFunctionsUnitOneAOV_files/image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAU ABgAgAAAAAAAAAIzhH+hyG0anHxrOmhvzQjzvn2AJ47hR4opCLVr4sbyTLdTHUlvtlv9feL8dEFe 0XcE5hoFADs= ------=_NextPart_01C8194E.037A7680 Content-Location: file:///C:/A5138E36/PolynomialFunctionsUnitOneAOV_files/image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAV 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content=3D"text/html; charset=3Dus-ascii"> <meta name=3DProgId content=3DWord.Document> <meta name=3DGenerator content=3D"Microsoft Word 11"> <meta name=3DOriginator content=3D"Microsoft Word 11"> <link id=3DMain-File rel=3DMain-File href=3D"../PolynomialFunctionsUnitOneA= OV.htm"> <![if IE]> <base href=3D"file:///C:\A5138E36\PolynomialFunctionsUnitOneAOV_files\heade= r.htm" id=3D"webarch_temp_base_tag"> <![endif]><o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"= /> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceType"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PlaceName"/> </head> <body lang=3DEN-US link=3Dblue vlink=3Dpurple> <div style=3D'mso-element:footnote-separator' id=3Dfs> <![if !supportFootnotes]> <hr align=3Dleft size=3D1 width=3D"33%"> <![endif]> </div> <div style=3D'mso-element:footnote-continuation-separator' id=3Dfcs> <![if !supportFootnotes]> <hr align=3Dleft size=3D1> <![endif]> </div> <div style=3D'mso-element:endnote-separator' id=3Des> <![if !supportFootnotes]> <hr align=3Dleft size=3D1 width=3D"33%"> <![endif]> </div> <div style=3D'mso-element:endnote-continuation-separator' id=3Decs> <![if !supportFootnotes]> <hr align=3Dleft size=3D1> <![endif]> </div> <div style=3D'mso-element:footer' id=3Df1> Tom Love= = &nb= sp; <st1:place w:st=3D"on"><st1:PlaceName w:st=3D"on">Malone</st1:PlaceN= ame> <st1:PlaceType w:st=3D"on">College</st1:PlaceType></st1:place> = &nb= sp; Fall 2003<o:p></o:p> </div> </body> </html> ------=_NextPart_01C8194E.037A7680 Content-Location: file:///C:/A5138E36/PolynomialFunctionsUnitOneAOV_files/image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkQBaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQCH AFIAgAAAAAAAAAL/BGKpy+0Po5y01oCs3rx7mxlY+JXmiSaYOpLpC8dMK9LyjaNttrv5D5TsasOg 8bjoHXo+pPPGXNqe1F+UWM3mlFitFzaarb7kU1jcLKsnZ/T6DRq74fRIOymvT+l3fJp89bbnx8fU 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