document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992558>Question 992558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain and range and sketch the graph for the functions f and g where f(x) is given by the polynomial below and g(x)=|f(x)|. Also use the graph to solve the inequality f(x)<0.\r<BR>\n" );
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document.write( "f(x)=9+3x-2x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612148 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52776)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Find the domain and range and sketch the graph for the functions f and g where f(x) is given by the polynomial below and g(x)=|f(x)|. <BR>\n" );
document.write( "Also use the graph to solve the inequality f(x)<0. <BR>\n" );
document.write( "f(x)=9+3x-2x^2<BR>\n" );
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document.write( "The domain of the function &nbsp;f&nbsp; is the entire number line, &nbsp;i.e. &nbsp;the set of all real numbers. &nbsp;(It is so for any polynomial). \r<BR>\n" );
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document.write( "The domain of the function &nbsp;g&nbsp; is the same entire number line, &nbsp;i.e. the set of all real numbers.\r<BR>\n" );
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document.write( "The plots of &nbsp;f&nbsp; and &nbsp;g&nbsp; are shown in the Figure below. &nbsp;The plot of &nbsp;g&nbsp; is in green. &nbsp;Partly it is over-posed the plot of &nbsp;f.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-5.5%2C+5.5%2C+-5.5%2C+10.5%2C%0D%0A++++++++++9%2B3x-2x%5E2%2C%0D%0A++++++++++abs%289%2B3x-2x%5E2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The roots of f are &nbsp;3&nbsp; and &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "f(x) < 0 &nbsp;in two semi-infinite intervals &nbsp;(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) &nbsp;and &nbsp;(3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >). \r<BR>\n" );
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document.write( " </SPAN>\n" );
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