document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124975>Question 124975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the methods in finding the range and domain of an equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91734 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=91734\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What are the methods in finding the range and domain of an equation?<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Here's an example:<BR>\n" );
document.write( "y = [sqrt(x-2)]/(x-5)<BR>\n" );
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document.write( "Domain:<BR>\n" );
document.write( "The denominator must not be zero, so x cannot be 5.<BR>\n" );
document.write( "The radicand cannot be negative, so x cannot be less than 2<BR>\n" );
document.write( "So the domain is (2,5)U(5,+inf)<BR>\n" );
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document.write( "Range:<BR>\n" );
document.write( "The easiest way to see the range is to graph the function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C30%2C-10%2C30%2C%28x-2%29%5E%281%2F2%29%2F%28x-5%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C30%2C-10%2C30%2C%28x-2%29%5E%281%2F2%29%2F%28x-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The range is all Real Numbers<BR>\n" );
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document.write( "If you had [sqrt(x-2)/(x-5)]^2 the domain would not<BR>\n" );
document.write( "change but the range would be all Real Numbers greater<BR>\n" );
document.write( "that or equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C30%2C-10%2C10%2C%28%28x-2%29%5E%281%2F2%29%2F%28x-5%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C30%2C-10%2C10%2C%28%28x-2%29%5E%281%2F2%29%2F%28x-5%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );