document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=52654>Question 52654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine if each of the following is a relation or a function. Tell why and give the domain and range of each one.\r<BR>\n" );
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document.write( "a) (0,1)(4,1)(6,2)(2,0)\r<BR>\n" );
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document.write( "b)  y=6 over 2x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35157 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) (0,1), (4,1), (6,2), (2,0)<BR>\n" );
document.write( "This is a function because for every x there is exactly one y.  Y's can have more than one x, but x's can have only one y.<BR>\n" );
document.write( "The Domain corresponds with the x values is {0,4,6,2}, the range corresponds with the y values is {1,1,2,0}<BR>\n" );
document.write( "b) y=6/(2x-1)<BR>\n" );
document.write( "This is a function.  When dealing with equations it is often easiest to look at y.  If it's not raised to an even power it's a function.<BR>\n" );
document.write( "For rational (fractions with variables in the denominator) functions the domain can be found by finding out what makes the denominator =0 (thus be undefined)<BR>\n" );
document.write( "2x-1=0<BR>\n" );
document.write( "2x-1+1=0+1<BR>\n" );
document.write( "2x=1<BR>\n" );
document.write( "2x/2=1/2<BR>\n" );
document.write( "x cannot = 1/2  <BR>\n" );
document.write( "Set builder notation:{x|x cannot=1/2}<BR>\n" );
document.write( "Interval notation: (- infinity, 1/2)U(1/2,+infinity)<BR>\n" );
document.write( "For the Range: y cannot eqaul 0.<BR>\n" );
document.write( "Set builder notation:{y|y cannot=0}<BR>\n" );
document.write( "Interval:(-infinity,0)U(0,+infinity)<BR>\n" );
document.write( "I don't know what math you're taking, so I don't want to tell you too much about how I know the range and freak you out.  Resubmit that portion with the level of math you're in and I'll tell you how to find out that y cannot = 0.  If you're in algebra, you can probably just plug it into your graphing calculator and look at what y can't be.  If your in precal or calculus, take the limit as x approaches infinity. </SPAN>\n" );
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