document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=670606>Question 670606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)={-2-x if x is less than or equal to 1<BR>\n" );
document.write( "     {-2+2x if x is > 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #417029 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20054)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=417029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)={-2-x if x is less than or equal to 1<BR>\n" );
document.write( "     {-2+2x if x is > 1\r<BR>\n" );
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document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28matrix%282%2C3%2C%0D%0A%0D%0A-2-x%2Cif%2Cx%3C=1%2C%0D%0A-2%2B2x%2Cif%2Cx%3E1%29%29 ALIGN=MIDDLE  ALT=\"system%28matrix%282%2C3%2C%0D%0A%0D%0A-2-x%2Cif%2Cx%3C=1%2C%0D%0A-2%2B2x%2Cif%2Cx%3E1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We plot the graphs of y = -2-x and the graph of y = -2+x \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-4%2C5%2C-5%2C4%2C+graph%28400%2C400%2C-4%2C5%2C-5%2C4%2C%28-2-x%29%0D%0A%0D%0A%0D%0A%0D%0A%29%2C%0D%0Agraph%28400%2C400%2C-4%2C5%2C-5%2C4%2C-2%2B2x%29%2C+locate%28-4%2C2.3%2Cy=-2-x%29%2C%0D%0Alocate%283%2C4%2Cy=-2%2B2x%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We chop off the line y = -2-x at x=2 and erase the part beyond that on the<BR>\n" );
document.write( "right because of x <u><</u> 1 tells us we can use only the portion of that line which is left of x=1\r<BR>\n" );
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document.write( "We chop off the line y = -2+2x at x=2 and erase the part beyond that on the<BR>\n" );
document.write( "left because of x > 1 tells us we can use only the portion of that line which is right of x = 1  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-4%2C5%2C-5%2C4%2C+graph%28400%2C400%2C-4%2C5%2C-5%2C4%2C%28-2-x%29%2Asqrt%281-x%29%2Fsqrt%281-x%29%0D%0A%0D%0A%0D%0A%0D%0A%29%2C%0D%0Agraph%28400%2C400%2C-4%2C5%2C-5%2C4%2C-2%2B2x%2Asqrt%28x-1%29%2Fsqrt%28x-1%29%29%2C+locate%28-4%2C2.3%2Cy=%28-2-x%29%0D%0A%0D%0A%0D%0A%29%2C%0D%0Alocate%283%2C4%2Cy=-2%2B2x%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But that's not all.  We must place a CLOSED circle at the end point of<BR>\n" );
document.write( "the graph of y=-2-x because of the inequality x<u><</u>1 and we must <BR>\n" );
document.write( "place an OPEN circle at the wnd point of of the graph of y = -2+2x because<BR>\n" );
document.write( "of the inequality x>1 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-4%2C5%2C-5%2C4%2C+graph%28400%2C400%2C-4%2C5%2C-5%2C4%2C%28-2-x%29%2Asqrt%28.96-x%29%2Fsqrt%28.96-x%29%29%2C+circle%281%2C-3%2C.1%29%2Ccircle%281%2C-3%2C.08%29%2Ccircle%281%2C-3%2C.07%29%2Ccircle%281%2C-3%2C.06%29%2Ccircle%281%2C-3%2C.02%29%2C%0D%0Agraph%28400%2C400%2C-4%2C5%2C-5%2C4%2C-2%2B2x%2Asqrt%28x-1.05%29%2Fsqrt%28x-1.05%29%29%2C+locate%28-4%2C2.3%2Cy=%28-2-x%29%29%2C%0D%0Acircle%281%2C0%2C.13%29%2C++++locate%283%2C4%2Cy=-2%2B2x%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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