document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126539>Question 1126539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box is formed by cutting squares from the four corners of a 9\"-wide by 12\"-long sheet of paper and folding up the sides.<BR>\n" );
document.write( "Let x represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches).<BR>\n" );
document.write( "A) Write a formula that expresses V in terms of x.<BR>\n" );
document.write( "B)Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula for f.<BR>\n" );
document.write( "C)What is the domain of f ? Enter your answer as an interval. <BR>\n" );
document.write( "D)What is the range of f ? Enter your answer as an interval.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743021 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=743021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x%289-2x%29%2812-2x%29 ALIGN=MIDDLE  ALT=\"v=x%289-2x%29%2812-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, volume\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=2x%289-2x%29%286-x%29%29 ALIGN=MIDDLE  ALT=\"highlight%28v=2x%289-2x%29%286-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "v will be positive between x at 0 and x at 6 but NOT including those boundary x values.\r<BR>\n" );
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document.write( "The zeros of v are  0, 6, and 8.5.<BR>\n" );
document.write( "NO value for x at nor above 6 can be accepted; beyond 8.5 will make one of the dimensions negative.  Between 6 and 8.5 would make volume v negative.\r<BR>\n" );
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document.write( "THe <b>domain</b> must be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C6 ALIGN=MIDDLE  ALT=\"0%3Cx%3C6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(Range,...   ...)\r<BR>\n" );
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document.write( "x for the extreme values would be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-sqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"%287-sqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2Bsqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"%287%2Bsqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   The one for the maximum v is the left-most x.\r<BR>\n" );
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document.write( "You can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%287-sqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%287-sqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to find maximum  range of v.  The minimum is greater than 0.\r<BR>\n" );
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document.write( "RANGE:  ( 0, 81.87 ]\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cv%3C=81.87 ALIGN=MIDDLE  ALT=\"0%3Cv%3C=81.87\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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