document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346763>Question 346763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y^2+x^2-4=0 .  what is the domain and what is the range ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247980 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><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=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y^(2)+x^(2)-4=0\r<BR>\n" );
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document.write( "Move all terms not containing x to the right-hand side of the equation.<BR>\n" );
document.write( "x^(2)=-y^(2)+4\r<BR>\n" );
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document.write( "Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.<BR>\n" );
document.write( "x=\~(-y^(2)+4)\r<BR>\n" );
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document.write( "First, substitute in the + portion of the \ to find the first solution.<BR>\n" );
document.write( "x=~(-y^(2)+4)\r<BR>\n" );
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document.write( "Next, substitute in the - portion of the \ to find the second solution.<BR>\n" );
document.write( "x=-~(-y^(2)+4)\r<BR>\n" );
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document.write( "The complete solution is the result of both the + and - portions of the solution.<BR>\n" );
document.write( "x=~(-y^(2)+4),-~(-y^(2)+4)\r<BR>\n" );
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document.write( "The domain of an expression is all real numbers except for the regions where the expression is undefined.  This can occur where the denominator equals 0, a square root is less than 0, or a logarithm is less than or equal to 0.  All of these are undefined and therefore are not part of the domain.<BR>\n" );
document.write( "(-y^(2)+4)<0\r<BR>\n" );
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document.write( "Solve the equation to find where the original expression is undefined.<BR>\n" );
document.write( "No Solution\r<BR>\n" );
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document.write( "The domain of the rational expression is all real numbers except where the expression is undefined.  In this case, there is no real number that makes the expression undefined.<BR>\n" );
document.write( "All real numbers\r<BR>\n" );
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document.write( "The domain of the inverse of y^(2)+x^(2)-4=0 is equal to the range of f(y)=sqrt(-y^(2)+4).<BR>\n" );
document.write( "Range: All real numbers </SPAN>\n" );
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