document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310822>Question 310822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) what do you mean by a rational number? Give an example of a rational number and an irrational number.\r<BR>\n" );
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document.write( "B) rewrite 0.32727272727 as a rational number.\r<BR>\n" );
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document.write( "C) Give an example of a rational function and a polynomial function.\r<BR>\n" );
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document.write( "D) differentiate a hole and an essential discontinuity of a function. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222295 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=222295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "A rational number is a number that can be expressed as the ratio of two integers.  An irrational number cannot be so expressed.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1278}{34567788}\"> is a rational number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4\"> is a rational number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{3}\"> is an irrational number.  It is also an algebraic number (it is the root of a non-constant polynomial equation with rational coefficients).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pi\"> is a transcendental irrational number (it is irrational AND it is NOT the root of any non-constant polynomial equation with rational coefficients)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{32727272727}{100000000000}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \frac{2x\ +\ 1}{(x\ +\ 2)^3}\"> is a rational function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ g(x)\ =\ \alpha_0x^n\ +\ \alpha_1x^{n-1}\ +\ \alpha_3x^{n-2}\ +\ \cdots\ +\ \alpha_{n-2}x^2\ +\ \alpha_{n-1}x\ +\ \alpha_n\"> is an <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\text{th}\"> degree polynomial equation if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \alpha_0\ \neq\ 0\"> \r<BR>\n" );
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document.write( "A hole is a hole in a graph. That is, a discontinuity that can be \"repaired\" by filling in a single point. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point.\r<BR>\n" );
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document.write( "Formally, a removable discontinuity is one at which the limit of the function exists but does not equal the value of the function at that point; this may be because the function does not exist at that point.\r<BR>\n" );
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document.write( "Essential Discontinuity\r<BR>\n" );
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document.write( "Any discontinuity that is not removable. That is, a place where a graph is not connected and cannot be made connected simply by filling in a single point. Step discontinuities and vertical asymptotes are two types of essential discontinuities.\r<BR>\n" );
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document.write( "Formally, an essential discontinuity is a discontinuity at which the limit of the function does not exist.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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