<HTML lang=en-x-mtfrom-zh><HEAD><script>(function(){var b=window,f="chrome";(function(){function g(a){this.t={};this.tick=function(a,d,c){this.t[a]=[void 0!=c?c:(new Date).getTime(),d];if(void 0==c)try{b.console.timeStamp("CSI/"+a)}catch(e){}};this.tick("start",null,a)}var a;b.performance&&(a=b.performance.timing);var h=a?new g(a.responseStart):new g;b.jstiming={Timer:g,load:h};if(a){var d=a.navigationStart,e=a.responseStart;0<d&&e>=d&&(b.jstiming.srt=e-d)}if(a){var c=b.jstiming.load;0<d&&e>=d&&(c.tick("_wtsrt",void 0,d),c.tick("wtsrt_","_wtsrt",e),c.tick("tbsd_","wtsrt_"))}try{a= null,b[f]&&b[f].csi&&(a=Math.floor(b[f].csi().pageT),c&&0<d&&(c.tick("_tbnd",void 0,b[f].csi().startE),c.tick("tbnd_","_tbnd",d))),null==a&&b.gtbExternal&&(a=b.gtbExternal.pageT()),null==a&&b.external&&(a=b.external.pageT,c&&0<d&&(c.tick("_tbnd",void 0,b.external.startE),c.tick("tbnd_","_tbnd",d))),a&&(b.jstiming.pt=a)}catch(k){}})();})(); </script><script src="http://translate.googleusercontent.com/translate/releases/twsfe_w_20150330_RC03/r/js/translate_c.js"></script><script>_intlStrings._originalText = "-NeSe:";_intlStrings._interfaceDirection="ltr";_intlStrings._interfaceAlign="left";_intlStrings._langpair="zh-CN|en";_intlStrings._feedbackUrl="http://translate.google.com/translate_suggestion";_intlStrings._currentBy="S_MRvы/f1u%2$s(W %1$s[bv";_intlStrings._unknown="ZO Tы";_intlStrings._suggestTranslation="f}Yvы^" ;_intlStrings._submit="cO^";_intlStrings._suggestThanks="a"`:N Google ыcOы^0";_intlStrings._reverse=false;</script><style type="text/css">.google-src-text {display: none !important} .google-src-active-text {display: block!important;color:black!important; font-size:12px!important;font-family:arial,sans-serif!important}.google-src-active-text a {font-size:12px!important}.google-src-active-text a:link {color:#00c!important;text-decoration:underline!important}.google-src-active-text a:visited {color:purple!important;text-decoration:underline!important}.google-src-active-text a:active {color:red!important;text-decoration:underline!important}</style><meta http-equiv="X-Translated-By" content="Google"><link href=http://drhuang.com/chinese/science/mathematics/handbook/a22/a22.htm hreflang=zh-CN rel="alternate machine-translated-from"><base href=http://drhuang.com/chinese/science/mathematics/handbook/a22/a22.htm /><META HTTP-EQUIV=Content-Type content="text/html; charset=UTF-8"><TITLE> Second, the power function and rational functions </TITLE></HEAD><BODY bgcolor=#ffffff><iframe src="http://translate.google.com.au/translate_un?depth=1&hl=zh-CN&rurl=translate.google.com.au&sl=zh-CN&tl=en&u=http://drhuang.com/chinese/science/mathematics/handbook/a22/a22.htm&lang=zh-CN&usg=ALkJrhjAFiwhxZT9JnS5N_E_juyOlWExQA" width=0 height=0 frameborder=0 style="width:0px;height:0px;border:0px;display:none;"></iframe><h3> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><FONT FACE="wiSO_GB2312" LANG=ZH-CN>N0B^QpeN gtQpe</font></font></span> <font face="[SO"><FONT FACE="wiSO_GB2312" LANG=ZH-CN>Second, the power function and rational functions</font></font></span> </h3><P ALIGN=JUSTIFY><P ALIGN=JUSTIFY></P><P ALIGN=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO">[ <FONT LANG=ZH-CN>[IN</font> ] <FONT LANG=ZH-CN>b_Y</font></font></span> <FONT LANG=ZH-CN><font face="[SO">[Definition] of the form</font></font></span> <FONT LANG=ZH-CN><font face="[SO"><IMG SRC=Image336.gif WIDTH=48 HEIGHT=25 align=absmiddle></font></font> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><FONT LANG=ZH-CN><font face="[SO">vQpey:NB^Qpe _-N</font></font> <FONT FACE="wiSO_GB2312" LANG=ZH-CN><FONT FACE=Symbol>a</font> <font face="[SO">:NNa[8^pe</font></font> <font face="[SO">.</font></span> <FONT LANG=ZH-CN><font face="[SO">Function called power function, wherein</font></font> <FONT FACE="wiSO_GB2312" LANG=ZH-CN><FONT FACE=Symbol>a</font> <font face="[SO">is an arbitrary real constant.</font></font></span> </P><P ALIGN=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><I>x</i> <FONT LANG=ZH-CN>vYy_</font></font></span> <font face="[SO"><FONT LANG=ZH-CN>polynomial</font> <I>x</i></font></span> </P><P ALIGN=CENTER> <FONT FACE="wiSO_GB2312" LANG=ZH-CN><IMG SRC=Image337.gif WIDTH=212 HEIGHT=24></font> </P><P ALIGN=RIGHT> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left">( <font face="Times New Roman, Times, serif"><I>a</i> <SUB>0</sub></font> , <font face="Times New Roman, Times, serif"><I>a</i> <SUB>1</sub></font> , <FONT FACE="MT Extra">L</font> , <font face="Times New Roman, Times, serif"><I>a <SUB>n</sub></i></font> <font face="[SO" lang=ZH-CN>:N8^pe </font> <font face="[SO"><font face="Times New Roman, Times, serif"><I>n</i></font> <FONT LANG=ZH-CN>:N6qpe</font> )</font></span> <font face="Times New Roman, Times, serif"><I>(A</i> <SUB>0,</sub> <I>a</i> <SUB>1,</sub></font> <FONT FACE="MT Extra">L,</font> <font face="Times New Roman, Times, serif"><I>a <SUB>n</sub></i></font> <font face="[SO" lang=ZH-CN>are constants,</font> <font face="[SO"><font face="Times New Roman, Times, serif"><I>n</i></font> <FONT LANG=ZH-CN>is a natural number)</font></font></span> </P><P ALIGN=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>y:N gtteQpe</font> <font face="[SO">.</font></span> <font face="[SO" lang=ZH-CN>Called rational entire <font face="[SO">function.</font></font></span> </P><P ALIGN=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>$N*NYy_vFU</font></span> <font face="[SO" lang=ZH-CN>Quotient of two polynomials</font></span> </P><P ALIGN=CENTER> <font face="[SO" lang=ZH-CN><IMG SRC=Image338.gif WIDTH=217 HEIGHT=48></font> </P><P ALIGN=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>y:N gtR_Qpe</font> <font face="[SO">.</font></span> <font face="[SO" lang=ZH-CN>Called Rational <font face="[SO">Functions.</font></font></span> </P><P ALIGN=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN> gtteQpeT gtR_Qpey:N gtQpe ge(u&{S</font> <font face="[SO"><font face="Times New Roman, Times, serif"><I>R</i> ( <I>x</i> )</font> <FONT LANG=ZH-CN>h:y</font> .</font></span> <font face="[SO" lang=ZH-CN>Rational and Rational Functions entire function known as rational functions, <FONT LANG=ZH-CN><font face="[SO">sometimes</font></font> denoted by the symbol</font> <font face="Times New Roman, Times, serif"><I><font face="[SO">R (x).</font></i></font></span> </P><P ALIGN=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO">[ <FONT LANG=ZH-CN>B^QpevVb_Nyr_</font> ]</font></span> <FONT LANG=ZH-CN><font face="[SO">[Graphics and features a power function]</font></font></span> </P><P ALIGN=JUSTIFY><P ALIGN=JUSTIFY></P><P ALIGN=JUSTIFY><FONT FACE="wiSO_GB2312" LANG=ZH-CN>0</FONT></P><table BORDER cellspacing=1 cellpadding=7 width=642><tr><td width=40% valign=TOP><p align=CENTER><span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>e zNVb_</font></span> <font face="[SO" lang=ZH-CN>Equations and graphics</font></span> </td><td width=60% valign=TOP><p align=CENTER> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>yr _</font> </span> <font face="[SO" lang=ZH-CN>Features</font></span> </td></tr><tr><td width=40% valign=TOP height=228><p align=CENTER><img src=1.gif width=182 height=187></td><td width=60% valign=TOP height=228><p align=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>f~Ǐp(0,0)T(1,1)S_</font> <font face="[SO"><i>x</i> &gt;1 <font lang=ZH-CN>e</font></font> <font face="wiSO_GB2312" lang=ZH-CN> <font face=Symbol>a</font> <font face="[SO">'Yf~ NGS_.</font></font></span> <font face="[SO" lang=ZH-CN>Curve through the point (0,0) and (1,1); <font face="[SO"><font lang=ZH-CN>when</font></font></font> <font face="[SO"><i>x&gt;</i></font> <font face="wiSO_GB2312" lang=ZH-CN><font face="[SO">1,</font> <font face=Symbol>a</font> <font face="[SO">larger the curve rises faster.</font></font></span> </p><p align=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>S_</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">:NvPpe Qpe:NvPQpe (W:S</font> (0, <font face=Symbol></font> ) <font face="[SO">-N:NXQpe (W:S</font> (- <font face=Symbol></font> ,0) <font face="Verdana, Arial, Helvetica, sans-serif">-N:NQQpe.</font></font></span> <font face="[SO" lang=ZH-CN>When</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">is an even number, the function is an even function, in the interval</font> (0, <font face=Symbol>)</font> <font face="[SO">for increasing function in the interval</font> (- <font face=Symbol>,</font> 0) <font face="Verdana, Arial, Helvetica, sans-serif">as a decreasing function.</font></font></span> </p><p align=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="Verdana, Arial, Helvetica, sans-serif" lang=ZH-CN>S_</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">:NGYpe Qpe:NGYQpeTXQpe.</font></font></span> <font face="Verdana, Arial, Helvetica, sans-serif" lang=ZH-CN>When</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">is odd, odd function for function and increasing function.</font></font></span> </td></tr><tr><td width=40% valign=TOP height=216><p align=CENTER><img src=2.gif width=170 height=173></td><td width=60% valign=TOP height=216><p align=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>f~Ǐp</font> <font face="wiSO_GB2312" lang=ZH-CN>(1,1).</font></span> <font face="[SO" lang=ZH-CN>Curve through the point</font> <font face="wiSO_GB2312" lang=ZH-CN>(1,1).</font></span> </p><p align=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>S_</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">:NvPpe Qpe:NvPQpe (W:S</font> (- <font face=Symbol></font> ,0) <font face="[SO">-N:NXQpe (W:S</font> (0, <font face=Symbol></font> ) <font face="[SO">-N:NQQpe.</font></font></span> <font face="[SO" lang=ZH-CN>When</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">negative even, function even function in the interval</font> (- <font face=Symbol>,</font> 0) <font face="[SO">for increasing function in the interval</font> (0, <font face=Symbol>)</font> <font face="[SO">for decreasing function.</font></font></span> </p><p align=JUSTIFY> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO" lang=ZH-CN>S_</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">:NGYpe Qpe:NGYQpeTQQpe.</font></font></span> <font face="[SO" lang=ZH-CN>When</font> <font face="wiSO_GB2312" lang=ZH-CN><font face=Symbol>a</font> <font face="[SO">negative odd function is an odd function and decreasing function.</font></font></span> </td></tr></table></BODY> <script>_addload(function(){_setupIW();_csi('zh-CN','en','http://drhuang.com/chinese/science/mathematics/handbook/a22/a22.htm');});</script></html>