document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637132>Question 637132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the function:  g(x) = 2/3 log_2(x-3) + 2 \r<BR>\n" );
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document.write( "Plot two points and the asymptotes  (if any) of the graph of the function. \r<BR>\n" );
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document.write( "Help please! Thank you very much! Can anyone please walk me through the steps to achieve this answer?! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401553 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=401553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Graph the function: g(x) = 2/3 log_2(x-3) + 2 <BR>\n" );
document.write( "Plot two points and the asymptotes (if any) of the graph of the function. <BR>\n" );
document.write( "I don't have the means to graph it for you, but I can describe how to do it.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "start with the basic log curve: y=logx (base 10)<BR>\n" );
document.write( "like all logx curves, regardless of base, they have the y-axis is an asymptote, and x-intercept=1.<BR>\n" );
document.write( "So this basic curve starts from (0,-&#8734;), crosses the x-axis at 1 and gradually increases to &#8734;.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given log curve: g(x) = 2/3 log_2(x-3) + 2<BR>\n" );
document.write( "Since it is a lower base(2), the curve is above the basic curve when <1, and below the basic curve when x>1.There is no change to the y-axis asymptote or x-intercept at 1.<BR>\n" );
document.write( "The 2/3 multiplier stretches the curve, making it more negative below the x-axis and more positive above the x-axis.<BR>\n" );
document.write( "(x-3) moves the asymptote and x-intercept 3 units to the right at x=3 and x=4 respectively<BR>\n" );
document.write( "Finally, +2 bumps the entire curve 2 units up<BR>\n" );
document.write( "..<BR>\n" );
document.write( "note:If you have a graphing calculator, it could greatly help you follow the steps above </SPAN>\n" );
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