document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=232209>Question 232209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the domain and range for the following Points?\r<BR>\n" );
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document.write( "{(1,3) (1,0) (1,-2) ( 1,8)}  And is it a function. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171664 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=171664\">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( "The domain is the set of values that can be taken by the independent or input variable -- generally the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.\r<BR>\n" );
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document.write( "You have four ordered pairs in your set, and all of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinates are equal to 1.  Therefore the domain is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{1\}\">.\r<BR>\n" );
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document.write( "The range is the set of all values of the dependent variable resulting from all values of the independent variable.  Therefore the range is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{-2,0,3,8\}\">, which are the four <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinates.\r<BR>\n" );
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document.write( "A relation is a function if and only if every element in the domain corresponds to one and only one element in the range.  Here you have the element 1 in the domain that corresponds to 4 different elements in the range.  Not a function.  If you graphed these four points, you would find that you would be able to draw a vertical line that would contain more than one of the points (in fact, the line would contain all four points).  Any time you can find such a vertical line, your relation is NOT a function.\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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