document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197822>Question 1197822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x)=[-x-3 , cubic root of x, x^2-x, x < -1, -1 < or equal x < 2, x > or equal 2<BR>\n" );
document.write( "Find f(-1), f(1), and f(2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831248 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Some of what you typed in is a bit garbled. But I'm assuming this is what the piecewise function should look like<BR>\n" );
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document.write( "If my assumption is incorrect, then please let me know.\r<BR>\n" );
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document.write( "That piecewise function breaks down into 3 cases.<BR>\n" );
document.write( "Case A: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-1 ALIGN=MIDDLE  ALT=\"x+%3C+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-x-3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "Case B: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C=x+%3C+2 ALIGN=MIDDLE  ALT=\"-1%3C=x+%3C+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "Case C: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=2 ALIGN=MIDDLE  ALT=\"x%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2-x ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can only pick exactly one case. This is because each interval mentioned has no overlap with any other. <BR>\n" );
document.write( "There's no way, for instance, to have x be something smaller than -1 and larger than 2 at the same time.\r<BR>\n" );
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document.write( "To compute f(-1) we plug in x = -1<BR>\n" );
document.write( "The input x = -1 fits the description of case B since -1 is in the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C=x%3C2 ALIGN=MIDDLE  ALT=\"-1%3C=x%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C=+-1%3C2 ALIGN=MIDDLE  ALT=\"-1+%3C=+-1%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a true statement.\r<BR>\n" );
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document.write( "We'll plug x = -1 into the second piece.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+root%283%2Cx%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=f%28-1%29+=+root%283%2C-1%29 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+root%283%2C-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=f%28-1%29+=+root%283%2C%28-1%29%5E3%29 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+root%283%2C%28-1%29%5E3%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=f%28-1%29+=+-1 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's compute f(1).\r<BR>\n" );
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document.write( "The input x = 1 fits the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C=x%3C2 ALIGN=MIDDLE  ALT=\"-1%3C=x%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we'll go for case B again.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+root%283%2Cx%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=f%281%29+=+root%283%2C1%29 ALIGN=MIDDLE  ALT=\"f%281%29+=+root%283%2C1%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=f%281%29+=+root%283%2C1%5E3%29 ALIGN=MIDDLE  ALT=\"f%281%29+=+root%283%2C1%5E3%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=f%281%29+=+1 ALIGN=MIDDLE  ALT=\"f%281%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lastly let's find f(2).<BR>\n" );
document.write( "The input x = 2 fits the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+2 ALIGN=MIDDLE  ALT=\"x+%3E=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "We'll go for case C this time.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2-x ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2-x\"   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=f%282%29+=+2%5E2-2 ALIGN=MIDDLE  ALT=\"f%282%29+=+2%5E2-2\"   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=f%282%29+=+2 ALIGN=MIDDLE  ALT=\"f%282%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<font color=red>Summary:</font><BR>\n" );
document.write( "f(-1) = -1<BR>\n" );
document.write( "f(1) = 1<BR>\n" );
document.write( "f(2) = 2<BR>\n" );
document.write( "</font> </SPAN>\n" );
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