document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042082>Question 1042082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem:<BR>\n" );
document.write( "Which of the following describes the end behavior of the equation below?<BR>\n" );
document.write( "F(x)=-x^3+3x^2<BR>\n" );
document.write( "a) As x decreases in value, f(x) decreases in value. As x increases in value, f(x) decreases in value.<BR>\n" );
document.write( "b) As x decreases in value, f(x) increases in value. As x increases in value, f(x) decreases in value.<BR>\n" );
document.write( "c) As x decreases in value, f(x) decreases in value. As x increases in value, f(x) increases in value.<BR>\n" );
document.write( "d) As x decreases in value, f(x) increases in value. As x increases in value, f(x) increases in value.<BR>\n" );
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document.write( "F(x)=-x^3+3x^2\r<BR>\n" );
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document.write( "The leading term is -x^3 since this term has the largest exponent. So the end behavior of F(x) will be the same end behavior of y = -x^3\r<BR>\n" );
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document.write( "As x heads off to negative infinity, this means F(x) is heading off to positive infinity. This is another way of saying \"as x decreases in value, y increases in value\".\r<BR>\n" );
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document.write( "As x heads off to positive infinity, this means F(x) is heading off to negative infinity. This is another way of saying \"as x increases in value, y decreases in value\".\r<BR>\n" );
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document.write( "So to sum things up, the answer is <BR>\n" );
document.write( "<font color=red size=4>As x decreases in value, f(x) increases in value. As x increases in value, f(x) decreases in value.</font>\r<BR>\n" );
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document.write( "So the answer is <font color=red size=4>Choice B)</font>\r<BR>\n" );
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document.write( "Here's a graph to visually verify things.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+0%2C-x%5E3%2B3x%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+0%2C-x%5E3%2B3x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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