document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121647>Question 121647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the inermediate value theorem to determine, if possible, whether g(x)=4x^3-3x+3 has a zero between -2 and -1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89301 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=89301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let's evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29 ALIGN=MIDDLE  ALT=\"g%28-2%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=g%28x%29=4x%5E3-3x%2B3 ALIGN=MIDDLE  ALT=\"g%28x%29=4x%5E3-3x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29=4%28-2%29%5E3-3%28-2%29%2B3 ALIGN=MIDDLE  ALT=\"g%28-2%29=4%28-2%29%5E3-3%28-2%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with -2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29=4%28-8%29-3%28-2%29%2B3 ALIGN=MIDDLE  ALT=\"g%28-2%29=4%28-8%29-3%28-2%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%5E3 ALIGN=MIDDLE  ALT=\"%28-2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get -8.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29=-32-3%28-2%29%2B3 ALIGN=MIDDLE  ALT=\"g%28-2%29=-32-3%28-2%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 4 and -8 to get  -32\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29=-32%2B6%2B3 ALIGN=MIDDLE  ALT=\"g%28-2%29=-32%2B6%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -3 and -2 to get  6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29=-23 ALIGN=MIDDLE  ALT=\"g%28-2%29=-23\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "-----------Now let's evaluate another value---------\r<BR>\n" );
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document.write( "Let's evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-1%29 ALIGN=MIDDLE  ALT=\"g%28-1%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=g%28x%29=4x%5E3-3x%2B3 ALIGN=MIDDLE  ALT=\"g%28x%29=4x%5E3-3x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-1%29=4%28-1%29%5E3-3%28-1%29%2B3 ALIGN=MIDDLE  ALT=\"g%28-1%29=4%28-1%29%5E3-3%28-1%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with -1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-1%29=4%28-1%29-3%28-1%29%2B3 ALIGN=MIDDLE  ALT=\"g%28-1%29=4%28-1%29-3%28-1%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E3 ALIGN=MIDDLE  ALT=\"%28-1%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get -1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-1%29=-4-3%28-1%29%2B3 ALIGN=MIDDLE  ALT=\"g%28-1%29=-4-3%28-1%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 4 and -1 to get  -4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-1%29=-4%2B3%2B3 ALIGN=MIDDLE  ALT=\"g%28-1%29=-4%2B3%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -3 and -1 to get  3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-1%29=2 ALIGN=MIDDLE  ALT=\"g%28-1%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "Since the y values transition from negative to positive as x goes from -2 to -1, this means there's a zero between -2 and -1 </SPAN>\n" );
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