document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208157>Question 1208157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the range with algebra (no graphing) of f(x)/g(x) if \r<BR>\n" );
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document.write( "f(x) = sqrt{4 - x^2}\r<BR>\n" );
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document.write( "g(x) = sqrt{9 - x^2} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846378 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=846378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The other tutors have done a great job. <BR>\n" );
document.write( "I know the instructions specifically state \"no graphing\", but let's look at a graph anyway to help verify the range is [0, 2/3] aka <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+y+%3C=+2%2F3 ALIGN=MIDDLE  ALT=\"0+%3C=+y+%3C=+2%2F3\"   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=graph%28400%2C400%2C-4%2C4%2C-1.5%2C1.5%2C-100%2C%28sqrt%284-x%5E2%29%29%2F%28sqrt%289-x%5E2%29%29%2C2%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The green curve is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29+=+%28f%28x%29%29%2F%28g%28x%29%29+=+%28sqrt%284-x%5E2%29%29%2F%28sqrt%289-x%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The blue horizontal line is y = 2/3 to help show the curve maxes out at this y value.\r<BR>\n" );
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document.write( "For some reason, the built-in algebra.com graphing tool shown above is glitching a bit. <BR>\n" );
document.write( "The part of the curve on the right needs to extend down to the point (2,0).<BR>\n" );
document.write( "Perhaps a better look would be to use something like Desmos<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.desmos.com/calculator/nxfzbzullv\">https://www.desmos.com/calculator/nxfzbzullv</a>\r<BR>\n" );
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document.write( "GeoGebra is another useful graphing tool.<BR>\n" );
document.write( "There are many others.<BR>\n" );
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