document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142094>Question 1142094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph below shows y=f(x). Show the final graph after the transformations of y=-2f(-x+3)+4.\r<BR>\n" );
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document.write( "Link to diagram : http://tinypic.com/r/2wp8rw3/9\r<BR>\n" );
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document.write( "Thank you in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762762 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=762762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You can do the graphing....<br><BR>\n" );
document.write( "You need to determine what the sequence of transformations does to each \"vertex\" of the graph.<br><BR>\n" );
document.write( "You first need to rewrite the transformation so that the expression in parentheses is of the form (x-a):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2f%28-x%2B3%29%2B4 ALIGN=MIDDLE  ALT=\"y+=+-2f%28-x%2B3%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2f%28-%28x-3%29%29%2B4 ALIGN=MIDDLE  ALT=\"y+=+-2f%28-%28x-3%29%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In that form, you can see the sequence of transformations is<br><BR>\n" );
document.write( "(1) (x-3) --> horizontal shift of 3<BR>\n" );
document.write( "(2) -(x-3) --> reflect in y-axis<BR>\n" );
document.write( "(3) -2f(-(x-3)) --> vertical stretch by -2 (reflect in x-axis and double)<BR>\n" );
document.write( "(4) -2f(-(x-3))+4 --> vertical shift of 4<br><BR>\n" );
document.write( "Now perform that sequence of transformations to each given point to find the image under the given transformation.<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "        A       B       C       D       E       F\r\n" );
document.write( " (0)  (-1,3)  (2,0)   (3,-3)  (4,2)   (6,1)   (8,-2)\r\n" );
document.write( " (1)   (2,3)  (5,0)   (6,-3)  (7,2)   (9,1)   (11,-2)\r\n" );
document.write( " (2)  (-2,3) (-5,0)  (-6,-3) (-7,2)  (-9,1)  (-11,-2)\r\n" );
document.write( " (3) (-2,-6) (-5,0)   (-6,6) (-7,-4) (-9,-2)  (-11,4)\r\n" );
document.write( " (4) (-2,-2) (-5,4)  (-6,10)  (-7,0)  (-9,2)  (-11,8)<br></PRE><BR>\n" );
document.write( "Those are the coordinates of the images of the original points under the given transformation. </SPAN>\n" );
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