document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976058>Question 976058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let a function f be defined by<BR>\n" );
document.write( "f(x) = x^2-2x-3/x^2+2x+3<BR>\n" );
document.write( "i) determine the domain of f(x)<BR>\n" );
document.write( "ii) find the range of f(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597806 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=597806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Like this:<BR>\n" );
document.write( "f(x) = (x^2-2x-3)/(x^2+2x+3)\r<BR>\n" );
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document.write( "Which will properly render as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2-2x-3%29%2F%28x%5E2%2B2x%2B3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2-2x-3%29%2F%28x%5E2%2B2x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Factor as much as possible.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%28x%2B1%29%29%2F%28x%5E2%2B2x%2B3%29 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%28x%2B1%29%29%2F%28x%5E2%2B2x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Only two critical x values.  Denominator is positive everywhere and has no real roots, so no<BR>\n" );
document.write( "vertical asymptotes.  Numerator gives f(x) its roots, which are  3 and -1.  The numerator is<BR>\n" );
document.write( "equivalent itself to a parabola, and in this example, f is negative between the roots and positive<BR>\n" );
document.write( "outside the interval which the roots bind.\r<BR>\n" );
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document.write( "Domain:  All real numbers.\r<BR>\n" );
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document.write( "The function f(x) is not a parabola.  There is a minimum, and a horizontal asymptote.  (Degree is two<BR>\n" );
document.write( "for both numerator and denominator).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28%2C%2C%2C%2C%2C%2CFactor+as+much+as+possible.%0D%0A%0D%0A%0D%0A%7B%7B%7B%28%28x-3%29%28x%2B1%29%29%2F%28x%5E2%2B2x%2B3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Only two critical x values.  Denominator is positive everywhere and has no real roots, so no<BR>\n" );
document.write( "vertical asymptotes.  Numerator gives f(x) its roots, which are  3 and -1.  The numerator is<BR>\n" );
document.write( "equivalent itself to a parabola, and in this example, f is negative between the roots and positive<BR>\n" );
document.write( "outside the interval which the roots bind.\r<BR>\n" );
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document.write( "Domain:  All real numbers.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "The function f(x) is not a parabola.  There is a minimum, and a horizontal asymptote.  (Degree is two<BR>\n" );
document.write( "for both numerator and denominator).\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%28x%5E2-2x-3%29%2F%28x%5E2%2B2x%2B3%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%28x%5E2-2x-3%29%2F%28x%5E2%2B2x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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