document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88740>Question 88740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not sure how to explain this: - completely confused\r<BR>\n" );
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document.write( "f(x)=[x3     x<1<BR>\n" );
document.write( "     [-1/2x2 +1.5   x>=1\r<BR>\n" );
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document.write( "Okay need to capture the equation from the [y=] then using graphing calculator make visual graphs for each compound function!!! - I havae no clue what this is talking about - OMG<BR>\n" );
document.write( "HELP!!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64512 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=64512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What this problem is telling you is:<BR>\n" );
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document.write( "First on the graph, for values of x that are less than 1 (that is,  for values to the left<BR>\n" );
document.write( "of +1 on the x-axis) the graph is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E3 ALIGN=MIDDLE  ALT=\"y+=+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "Next on the graph, for values of x that are greater than 1 (that is, for values at or to <BR>\n" );
document.write( "the right of +1 on the x-axis, the graph follows the path of the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%5E2+%2B+1.5 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%5E2+%2B+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Let's begin by graphing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E3 ALIGN=MIDDLE  ALT=\"y+=+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This graph is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since this graph only applies for values of x that are less than +1, imagine that you take<BR>\n" );
document.write( "an eraser and wipe out that part of the graph that goes upward above the values of y = 1<BR>\n" );
document.write( "so that the graph looks like:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C1%2C-10%2C10%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C1%2C-10%2C10%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next let's graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%5E2+%2B+1.5 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%5E2+%2B+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This graph is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%5E2%2B+1.5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x%5E2%2B+1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But this graph only applies when the value of x is 1 or is greater than 1. So imagine<BR>\n" );
document.write( "that you erase that part of the graph where x is to the left of +1.  After the erasure the<BR>\n" );
document.write( "graph would look like:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C1%2C10%2C-10%2C10%2C%28-1%2F2%29x%5E2%2B+1.5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C1%2C10%2C-10%2C10%2C%28-1%2F2%29x%5E2%2B+1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's put both graphs on the same set of coordinate axes.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2C%28-1%2F2%29x%5E2%2B+1.5%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2C%28-1%2F2%29x%5E2%2B+1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The \"combined\" graph that is the answer you need is that graph that follows the red part <BR>\n" );
document.write( "until x is just barely less than 1.  That is, the graph that rises from minus infinity, <BR>\n" );
document.write( "goes through the origin and then rises to the point where x is just less than -1 and y is<BR>\n" );
document.write( "just less than -1. (For this problem, that point appears to be where the red and green graphs<BR>\n" );
document.write( "intersect.)  After that point, as x gets more positive the graph that is the answer you<BR>\n" );
document.write( "are looking for follows the green path, going downward, crossing the x-axis where x is<BR>\n" );
document.write( "approximately +1.73, and continuing down toward minus infinity in the y direction.<BR>\n" );
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document.write( "So, in summary, what you do for this problem is to find the appropriate pieces of two<BR>\n" );
document.write( "graphs and visualize them as one \"put together\" graph.  Note that in other problems you<BR>\n" );
document.write( "will encounter, the two pieces may not intersect as they do in this problem.  Where they<BR>\n" );
document.write( "approach each other there may be a \"jump\" in y values which means the two graphs are not<BR>\n" );
document.write( "continuous. In this problem, they are continuous, so the resulting graph looks a little nicer.<BR>\n" );
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document.write( "Hope this helps you to understand what the problem is asking for you to do.<BR>\n" );
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