document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4873>Question 4873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am completely stuck on this problem.  Help!\r<BR>\n" );
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document.write( "Graph the fuction:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g+%28x%29=+3+%2Alog%282%2C%28x-7%29%29 ALIGN=MIDDLE  ALT=\"g+%28x%29=+3+%2Alog%282%2C%28x-7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<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 #2380 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> graphing....learn the basic shapes first then apply that knowledge to more complicated ones. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%5Ex ALIGN=MIDDLE  ALT=\"y=2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or any exponential function) looks like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-4%2C5%2C-6%2C40%2C+2%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-4%2C5%2C-6%2C40%2C+2%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note 2 things:\r<BR>\n" );
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document.write( "1. it does not go below the x-axis, since there is no value of x that can make y negative. In fact as x becomes more negative, the curve approaches the x-axis, ie approaches y=0. This \"approaching, but never quite reaching\" characteristic is called the asymptote.\r<BR>\n" );
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document.write( "2. the curve rises rapidly to infinity as x increases.\r<BR>\n" );
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document.write( "So, what about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%5E4x%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%5E4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >? First thing is USE BRACKETS!!!! because i do not know if you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%5E%284x%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%5E%284x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%5E%284x%29%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%5E%284x%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So i shall do both!\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%5E%284x%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%5E%284x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we know the rough shape. Just need to know the asymptote and any values where the curve crosses the axes.\r<BR>\n" );
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document.write( "Any value of x gives a whole range of possible values of 4x+4. All of these, as powers of 2 will never give a negative answer for y. So the curve, again, does not go below the x-axis...ie the asymptote is y=0.\r<BR>\n" );
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document.write( "Voila, all we need now is find where the curve crosses the y=axis (ie where x=0)... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5E%284x%2B4%29 ALIGN=MIDDLE  ALT=\"y+=+2%5E%284x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5E%284%280%29%2B4%29 ALIGN=MIDDLE  ALT=\"y+=+2%5E%284%280%29%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5E4 ALIGN=MIDDLE  ALT=\"y+=+2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> y=16.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-2%2C1%2C-3%2C300%2C+2%5E%284x%2B4%29%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-2%2C1%2C-3%2C300%2C+2%5E%284x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "see how this is exactly the same type of curve but the axes scales are hugely different.\r<BR>\n" );
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document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%5E%284x%29%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%5E%284x%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again, we know the rough shape..any value of x will never give a negative answer, so never below y=0. However, we then add 4 to all answers, so our asymptote is now no longer y=0, but y=4.\r<BR>\n" );
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document.write( "Find where the curve crosses the y-axis (where x=0)...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%5E%284x%29%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%5E%284x%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29+=+y+=+2%5E%280%29%2B4 ALIGN=MIDDLE  ALT=\"f%280%29+=+y+=+2%5E%280%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1%2B4 ALIGN=MIDDLE  ALT=\"y+=+1%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> y=5\r<BR>\n" );
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document.write( "Hope this all helps. Learn the following basic shapes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+log%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+log%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "More complex versions of each type have their own characters but at least it is a start :-)\r<BR>\n" );
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document.write( "jon<BR>\n" );
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