document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199726>Question 1199726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given f(x) = 3/4x + 2, and g(x) = 1/2 • f(x) + 3. Describe the transformations(list them) and write the new simplified equation for g(x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833689 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=833689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "g(x) = (1/2) * f(x) + 3<br><BR>\n" );
document.write( "The \"1/2\" shrinks the graph vertically by a factor of 1/2.<BR>\n" );
document.write( "The \"+3\" shifts the graph up 3 units.<br><BR>\n" );
document.write( "A graph, showing the transformations:<br><BR>\n" );
document.write( "red: f(x) = (3/4)x+2<BR>\n" );
document.write( "green: (1/2) * f(x): red, shrunk vertically by a factor of 1/2<BR>\n" );
document.write( "blue: (1/2) * f(x) + 3: green, shifted up 3 units<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-14%2C6%2C-5%2C5%2C%283%2F4%29x%2B2%2C%283%2F8%29x%2B1%2C%283%2F8%29x%2B4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation of the new graph is<br><BR>\n" );
document.write( "g(x) = (1/2)(f(x))+3<BR>\n" );
document.write( "g(x) = (1/2)((3/4)x+2)+3<BR>\n" );
document.write( "g(x) = ((3/8)x+1)+3<BR>\n" );
document.write( "g(x) = (3/8)x+4<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );