document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128744>Question 1128744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of <BR>\n" );
document.write( "f(x) = 1/ 3^- x is reflected about the y-axis and compressed vertically by a factor of 1/4. <BR>\n" );
document.write( " What is the equation of the new function, g(x)? \r<BR>\n" );
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document.write( "*I thought the answer would be 1/4 (x-1/3^-x), assuming that the vertical compression variable goes outside of the parentheses and 1/3^x-3 goes inside the equation. This however was wrong. Can someone explain how setting up these types of equations should be done, especially for future references? Thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745241 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13350)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745241\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "To begin with, the given function is in a very unusual form.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283%5E%28-x%29%29+=+3%5Ex ALIGN=MIDDLE  ALT=\"1%2F%283%5E%28-x%29%29+=+3%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "But we can, nevertheless, work the problem with the function as given.<br><BR>\n" );
document.write( "The vertical compression factor becomes a factor outside the parentheses, as you say.<br><BR>\n" );
document.write( "But what you are doing with the reflection about the y axis makes no sense.  Reflecting a function about the y axis changes x to the opposite of x.<br><BR>\n" );
document.write( "So a reflection of f(x) = 1/3^(-x) about the y axis and a compression vertically by a factor of 1/4 yields<br><BR>\n" );
document.write( "g(x) = (1/4)(1/(3^x))<br><BR>\n" );
document.write( "Graphs of f(x) (red) and g(x) (green):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-6%2C6%2C-2%2C10%2C1%2F%283%5E%28-x%29%29%2C%281%2F4%29%281%2F%283%5Ex%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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