document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173883>Question 173883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you change the functions below to make them easier to graph? It is possible to just look that the functions as it is and understand how the graph will look like, in terms of the x and y points?\r<BR>\n" );
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document.write( "Y=log_2^(4x)<BR>\n" );
document.write( "Y=log_2^(x^2)<BR>\n" );
document.write( "Y=log_2(x-2)<BR>\n" );
document.write( "Y=log_2(x^-1)\r<BR>\n" );
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document.write( "Log_2 means to the base of 2.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129102 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%282%2C%28x%5E%28-1%29%29%29 ALIGN=MIDDLE  ALT=\"y+=+log%282%2C%28x%5E%28-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can rewrite this as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ey+=+1%2Fx ALIGN=MIDDLE  ALT=\"2%5Ey+=+1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If I plot <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+1%2Fy ALIGN=MIDDLE  ALT=\"2%5Ex+=+1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5E%28-x%29 ALIGN=MIDDLE  ALT=\"y+=+2%5E%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "instead, this<BR>\n" );
document.write( "is the inverse function and will be symmetrical<BR>\n" );
document.write( "with the original function  about <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;\" >.<BR>\n" );
document.write( "I'll plot both to prove it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Clog%282%2C1%2Fx%29%2C+2%5E%28-x%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Clog%282%2C1%2Fx%29%2C+2%5E%28-x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As for which is which, The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5E%28-x%29 ALIGN=MIDDLE  ALT=\"y+=+2%5E%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has the points<BR>\n" );
document.write( "(-1,2), (0,1), (1,1/2)<BR>\n" );
document.write( "You can apply this method to the others also  </SPAN>\n" );
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