document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134359>Question 134359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem. Thank You!\r<BR>\n" );
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document.write( "Graph the function.\r<BR>\n" );
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document.write( "f(x)= 4x+2, if x<-2<BR>\n" );
document.write( "      x   , if -2(less than or equal to sign) x (less than or equal to sign) 3<BR>\n" );
document.write( "      3x-1, if x>3<BR>\n" );
document.write( "everything after the equals sign are in one bracket ({)<BR>\n" );
document.write( "Please help me-I keep getting this wrong on my assignments and tests. Thank You! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98264 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=98264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of <a  rel=nofollow HREF=http://www.mozilla.com/en-US/firefox/>Firefox</a> to see these images.\r<BR>\n" );
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document.write( "Let's break up this piecewise function into 3 pieces\r<BR>\n" );
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document.write( "Piece # 1: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%2B2 ALIGN=MIDDLE  ALT=\"y=4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%2B2 ALIGN=MIDDLE  ALT=\"y=4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (tell me if you need help with graphing)\r<BR>\n" );
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document.write( "Now let's <b>only</b> draw the part of the graph that is less than x=-2. In other words, erase everything to the right of x=-2 for the graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%2B2 ALIGN=MIDDLE  ALT=\"y=4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Piece # 2:\r<BR>\n" );
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document.write( "Now let's graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=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=graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cx%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now since we have the condition <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3C=x%3C=3 ALIGN=MIDDLE  ALT=\"-2%3C=x%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that our new graph should look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%29%2C%0D%0Acircle%28-1.6%2C-1.6%2C0.05%29%2C%0D%0Aline%28-1.6%2C-1.6%2C-1.2%2C-1.2%29%2C%0D%0Acircle%28-1.2%2C-1.2%2C0.05%29%2C%0D%0Aline%28-1.2%2C-1.2%2C-0.799999999999996%2C-0.799999999999996%29%2C%0D%0Acircle%28-0.799999999999996%2C-0.799999999999996%2C0.05%29%2C%0D%0Aline%28-0.799999999999996%2C-0.799999999999996%2C-0.399999999999996%2C-0.399999999999996%29%2C%0D%0Acircle%28-0.399999999999996%2C-0.399999999999996%2C0.05%29%2C%0D%0Aline%28-0.399999999999996%2C-0.399999999999996%2C0%2C0%29%2C%0D%0Acircle%280%2C0%2C0.05%29%2C%0D%0Aline%280%2C0%2C0.400000000000004%2C0.400000000000004%29%2C%0D%0Acircle%280.400000000000004%2C0.400000000000004%2C0.05%29%2C%0D%0Aline%280.400000000000004%2C0.400000000000004%2C0.800000000000004%2C0.800000000000004%29%2C%0D%0Acircle%280.800000000000004%2C0.800000000000004%2C0.05%29%2C%0D%0Aline%280.800000000000004%2C0.800000000000004%2C1.2%2C1.2%29%2C%0D%0Acircle%281.2%2C1.2%2C0.05%29%2C%0D%0Aline%281.2%2C1.2%2C1.6%2C1.6%29%2C%0D%0Acircle%281.6%2C1.6%2C0.05%29%2C%0D%0Aline%281.6%2C1.6%2C2%2C2%29%2C%0D%0Acircle%282%2C2%2C0.05%29%2C%0D%0Aline%282%2C2%2C2.4%2C2.4%29%2C%0D%0Acircle%282.4%2C2.4%2C0.05%29%2C%0D%0Aline%282.4%2C2.4%2C2.8%2C2.8%29%2C%0D%0Acircle%282.8%2C2.8%2C0.05%29%2C%0D%0Aline%282.8%2C2.8%2C3.2%2C3.2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from x=-2 to x=3\r<BR>\n" );
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document.write( "Piece #3 \r<BR>\n" );
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document.write( "Now let's graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-1 ALIGN=MIDDLE  ALT=\"y=3x-1\"   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=graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C3x-1%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C3x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now because the corresponding inequality is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E3 ALIGN=MIDDLE  ALT=\"x%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that we <b>only</b> draw the part of the graph that is greater than 3\r<BR>\n" );
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document.write( "So the graph should look like\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%29%2C%0D%0Acircle%283.2%2C8.6%2C0.05%29%2C%0D%0Aline%283.2%2C8.6%2C3.6%2C9.8%29%2C%0D%0Acircle%283.6%2C9.8%2C0.05%29%2C%0D%0Aline%283.6%2C9.8%2C4%2C11%29%2C%0D%0Acircle%284%2C11%2C0.05%29%2C%0D%0Aline%284%2C11%2C4.4%2C12.2%29%2C%0D%0Acircle%284.4%2C12.2%2C0.05%29%2C%0D%0Aline%284.4%2C12.2%2C4.80000000000001%2C13.4%29%2C%0D%0Acircle%284.80000000000001%2C13.4%2C0.05%29%2C%0D%0Aline%284.80000000000001%2C13.4%2C5.20000000000001%2C14.6%29%2C%0D%0Acircle%285.20000000000001%2C14.6%2C0.05%29%2C%0D%0Aline%285.20000000000001%2C14.6%2C5.60000000000001%2C15.8%29%2C%0D%0Acircle%285.60000000000001%2C15.8%2C0.05%29%2C%0D%0Aline%285.60000000000001%2C15.8%2C6.00000000000001%2C17%29%2C%0D%0Acircle%286.00000000000001%2C17%2C0.05%29%2C%0D%0Aline%286.00000000000001%2C17%2C6.40000000000001%2C18.2%29%2C%0D%0Acircle%286.40000000000001%2C18.2%2C0.05%29%2C%0D%0Aline%286.40000000000001%2C18.2%2C6.80000000000001%2C19.4%29%2C%0D%0Acircle%286.80000000000001%2C19.4%2C0.05%29%2C%0D%0Aline%286.80000000000001%2C19.4%2C7.20000000000001%2C20.6%29%2C%0D%0Acircle%287.20000000000001%2C20.6%2C0.05%29%2C%0D%0Aline%287.20000000000001%2C20.6%2C7.60000000000001%2C21.8%29%2C%0D%0Acircle%287.60000000000001%2C21.8%2C0.05%29%2C%0D%0Aline%287.60000000000001%2C21.8%2C8.00000000000001%2C23%29%2C%0D%0Acircle%288.00000000000001%2C23%2C0.05%29%2C%0D%0Aline%288.00000000000001%2C23%2C8.40000000000001%2C24.2%29%2C%0D%0Acircle%288.40000000000001%2C24.2%2C0.05%29%2C%0D%0Aline%288.40000000000001%2C24.2%2C8.80000000000001%2C25.4%29%2C%0D%0Acircle%288.80000000000001%2C25.4%2C0.05%29%2C%0D%0Aline%288.80000000000001%2C25.4%2C9.20000000000001%2C26.6%29%2C%0D%0Acircle%289.20000000000001%2C26.6%2C0.05%29%2C%0D%0Aline%289.20000000000001%2C26.6%2C9.60000000000001%2C27.8%29%2C%0D%0Acircle%289.60000000000001%2C27.8%2C0.05%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-1 ALIGN=MIDDLE  ALT=\"y=3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > from x=3 to infinity\r<BR>\n" );
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document.write( "Now let's combine the three graphs and plot them on the same coordinate system\r<BR>\n" );
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document.write( "Graph of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=\left\{ 4x+2 \text{ if x<-2} \\  x \text{ if -2\le x\le3} \\ 3x-1 \text{ if x>3}\">\r<BR>\n" );
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