document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939711>Question 939711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey! I am working on finding the domain and range of a relation that is not a function. The relation is: 4(x-1)^2+16y^2=32.<BR>\n" );
document.write( "For domain, I have tried solving for y and got y^2=[-(x-1)^2]/(4)+2. The next step would be square rooting to get the equation under the square radical and taking that equation to put in an inequality. The problem is that the equation is negative, making it undefined over reals. The same problem occurs when solving for the range. Please help me, thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572668 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> domain:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-1%29%5E2%2B16y%5E2=32 ALIGN=MIDDLE  ALT=\"4%28x-1%29%5E2%2B16y%5E2=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16y%5E2=32-4%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"16y%5E2=32-4%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=32%2F16-4%28x-1%29%5E2%2F16 ALIGN=MIDDLE  ALT=\"y%5E2=32%2F16-4%28x-1%29%5E2%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=2-%281%2F4%29%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"y%5E2=2-%281%2F4%29%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%282-%281%2F4%29%28x-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"y=sqrt%282-%281%2F4%29%28x-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ; to have real solution, determinante\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-%281%2F4%29%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"2-%281%2F4%29%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be greater or equal to zero\r<BR>\n" );
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document.write( "so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-%281%2F4%29%28x-1%29%5E2%3E=0 ALIGN=MIDDLE  ALT=\"2-%281%2F4%29%28x-1%29%5E2%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3E=%281%2F4%29%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"2%3E=%281%2F4%29%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%3E=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"8%3E=%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%29%3E=x-1 ALIGN=MIDDLE  ALT=\"sqrt%288%29%3E=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%282%2A4%29%3E=x ALIGN=MIDDLE  ALT=\"1%2Bsqrt%282%2A4%29%3E=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2sqrt%282%29%3E=x ALIGN=MIDDLE  ALT=\"1%2B2sqrt%282%29%3E=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >...since for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have positive and negative solution,\r<BR>\n" );
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document.write( "means, solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2sqrt%282%29%3E=x ALIGN=MIDDLE  ALT=\"1%2B2sqrt%282%29%3E=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2sqrt%282%29%3C=x ALIGN=MIDDLE  ALT=\"1-2sqrt%282%29%3C=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain is:\r<BR>\n" );
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document.write( "{  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2sqrt%282%29%3C=x%3C=1%2B2sqrt%282%29 ALIGN=MIDDLE  ALT=\"1-2sqrt%282%29%3C=x%3C=1%2B2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  }<BR>\n" );
document.write( "(assuming a function from reals to reals)\r<BR>\n" );
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document.write( "to find the range, find out what is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes from zero to infinity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%282-%281%2F4%29%28x-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"y=sqrt%282-%281%2F4%29%28x-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes greater, and the smallest value of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28x-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28x-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > could be  zero, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%282%29 ALIGN=MIDDLE  ALT=\"y=sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the range is:\r<BR>\n" );
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document.write( "{  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=y%3C=sqrt%282%29 ALIGN=MIDDLE  ALT=\"0%3C=y%3C=sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  }\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );