document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000357>Question 1000357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Plz help me to explaain the range of this quadratic equation.{f(x)=1÷sqrt(x^2-2x-3)} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617835 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=617835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That is a rational function, and not a quadratic equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2Fsqrt%28x%5E2-2x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2Fsqrt%28x%5E2-2x-3%29\"   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=x%5E2-2x-3 ALIGN=MIDDLE  ALT=\"x%5E2-2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Make the two critical values for x,  -1, and +3.<BR>\n" );
document.write( "x must not be between those values but can be at either of them.\r<BR>\n" );
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document.write( "The denominator of the function will never be negative, so f will never be negative.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-3 ALIGN=MIDDLE  ALT=\"x%5E2-2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be very near to 0, but it must never become 0 in the function because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2-2x-3%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2-2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the denominator.  Now, according to this requirement,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-1 ALIGN=MIDDLE  ALT=\"x%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E3 ALIGN=MIDDLE  ALT=\"x%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "As x approaches either critical x value,  f tends toward positive infinity, no bound.  As x goes infinitely to the left or infinitely to the right, f approaches but never reaches 0.   \r<BR>\n" );
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document.write( "The RANGE for f(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%3E0 ALIGN=MIDDLE  ALT=\"f%28x%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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