document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166616>Question 1166616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose the graph of f is given. describe how the graph of each function can be obtained from the graph of f. do not graph. \r<BR>\n" );
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document.write( "y=2f (x-2) +2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791124 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=791124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=f%28x%29 ALIGN=MIDDLE  ALT=\"y=f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2f%28x-2%29%2B2 ALIGN=MIDDLE  ALT=\"y=2f%28x-2%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The \"2f\" doubles the y value (stretches the graph vertically by a factor of 2);<BR>\n" );
document.write( "The (x-2) moves the graph 2 units to the RIGHT;<BR>\n" );
document.write( "The +2 moves the graph up 2 units.<br><BR>\n" );
document.write( "The order of the transformations is always the order in which you would evaluate the function for a given input value of x.  That order is<br><BR>\n" );
document.write( "(1) f(x-2), so move the graph 2 units to the right;<BR>\n" );
document.write( "(2) 2f(x-2), so stretch the graph vertically by a factor of 2; and<BR>\n" );
document.write( "(3) 2f(x-2)+2, so move the graph up 2 units.<br><BR>\n" );
document.write( "Short summary: The graph is moved 2 units to the right, then stretched vertically by a factor of 2, and then moved up 2 units.<br><BR>\n" );
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