document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996105>Question 996105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you find out the largest and the smallest values for (a) x^2 + y^2 (b) x^2 - y^2 if -10 <= x <= 10 and -5 <= y <= 5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614667 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=614667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)\r<BR>\n" );
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document.write( "If f(x) = x^2 and the domain is restricted to [-10,10], then the range is [0,100]. 0 is the smallest output, 100 is the largest<BR>\n" );
document.write( "x^2 maxes out at 100\r<BR>\n" );
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document.write( "If f(x) = x^2 and the domain is restricted to [-5,5], then the range is [0,25]. 0 is the smallest output, 25 is the largest<BR>\n" );
document.write( "y^2 maxes out at 25\r<BR>\n" );
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document.write( "Overall, x^2 + y^2 will max out to 100+25 = 125\r<BR>\n" );
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document.write( "The smallest x^2 can get is 0 (see above)<BR>\n" );
document.write( "The smallest y^2 can get is 0 (see above)<BR>\n" );
document.write( "The smallest x^2+y^2 can get is 0+0 = 0\r<BR>\n" );
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document.write( "Summary: <BR>\n" );
document.write( "largest value = 125<BR>\n" );
document.write( "smallest value = 0<BR>\n" );
document.write( "0 <= x^2+y^2 <= 125\r<BR>\n" );
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document.write( "(b)\r<BR>\n" );
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document.write( "Look back at part (a) to find that x^2 maxes out at 100<BR>\n" );
document.write( "the smallest y^2 gets is 0<BR>\n" );
document.write( "x^2 - y^2 maxes out at 100-0 = 100\r<BR>\n" );
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document.write( "The smallest x^2 gets is 0<BR>\n" );
document.write( "The largest y^2 gets is 25<BR>\n" );
document.write( "0-25 = -25<BR>\n" );
document.write( "The smallest x^2 - y^2 gets is -25\r<BR>\n" );
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document.write( "Summary: <BR>\n" );
document.write( "largest value = 100<BR>\n" );
document.write( "smallest value = -25<BR>\n" );
document.write( "-25 <= x^2-y^2 <= 100 </SPAN>\n" );
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