document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179180>Question 179180</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780131572256/algebrahomeworkh>College Mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am looking for the domain and the range for the equation:  x^2+y = 10\r<BR>\n" );
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document.write( "I thought that the square root of a negative number was imaginary and, as such we could not have a function from this equation.  Apparently, this is not correct.  Can you please explain what are and how to find the domain and range here? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134126 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=134126\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> write this as y=-x^2+10<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x%5E2%2B10%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x%5E2%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the domain (input values) x values in this case is all real numbers<BR>\n" );
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document.write( "the range (output values) y values in this case is much more difficult to determine normally.<BR>\n" );
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document.write( "try solving for x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-y%2B10 ALIGN=MIDDLE  ALT=\"x%5E2=-y%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > this doesnt always work but at times it does, and is a good starting point.<BR>\n" );
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document.write( "x= + or -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-y%2B10%29 ALIGN=MIDDLE  ALT=\"sqrt%28-y%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > since we cant have a negative number inside the square root sign ,this does limit the range. -y+10 has to be greater than or equal to  zero.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%2B10%3E=0 ALIGN=MIDDLE  ALT=\"-y%2B10%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%3E=-10 ALIGN=MIDDLE  ALT=\"-y%3E=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=10 ALIGN=MIDDLE  ALT=\"y%3C=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........remember that when you divide or multiply an inequality by a negative number you need to reverse the sign.....<BR>\n" );
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document.write( "so {y:y<=10} is the range...so all reals less than 10. y cannot for instance take on the value 12 otherwise you would have 12=-x^2+10<BR>\n" );
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document.write( "2=-x^2<BR>\n" );
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document.write( "x^2=-2...and we know that wont work... </SPAN>\n" );
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