document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066486>Question 1066486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) = &#8730;x. Write the equation for the final transformed graph if the following<BR>\n" );
document.write( "transformations are applied to f, in the following order: stretch horizontally by a factor<BR>\n" );
document.write( "of 2; shift downward by 5 units; shift right by 3 units.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #682116 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=682116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's a good reference on transformations.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://cms.cerritos.edu/uploads/pmata/Math%20140%20Materials/Chapter%201/1.7_Transformations.pdf\" target = \"_blank\">http://cms.cerritos.edu/uploads/pmata/Math%20140%20Materials/Chapter%201/1.7_Transformations.pdf</a>\r<BR>\n" );
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document.write( "your equation is y = sqrt(x).\r<BR>\n" );
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document.write( "it is shown below with check points at x = 4 and x = 16.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/020502.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "it will be easier to see the transformations if we stretch it first.\r<BR>\n" );
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document.write( "your stretched equation is y = sqrt(x/2)\r<BR>\n" );
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document.write( "it is shown below with check points at x = 8 and x = 32.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/020503.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "your stretched equation shifted down 5 units is y = sqrt(x/2)-5.\r<BR>\n" );
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document.write( "it is shown below with check points at x = 8 and x = 32.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/020504.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "your stretched equation shifgted down 5 units and then shifter right 3 units is y = sqrt((x-3)/2)-5\r<BR>\n" );
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document.write( "it is shown below with check points at x = 11 and x = 35.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/020505.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the original checkpoints are at x = 4 and x = 16.<BR>\n" );
document.write( "when x = 4,sqrt(x) = 2<BR>\n" );
document.write( "when x = 16, sqrt(x) = 4\r<BR>\n" );
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document.write( "when you stretch it by a factor of 2, the checkpoints becomes x = 8 and x = 32.<BR>\n" );
document.write( "when x = 8, sqrt(x) = 2<BR>\n" );
document.write( "when x = 32, sqrt(x) = 4\r<BR>\n" );
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document.write( "when you shift it down by 5, the check points remain at x = 8 and x = 32.<BR>\n" );
document.write( "when x = 8, sqrt(x) = 2 - 5 = -3<BR>\n" );
document.write( "when x = 32, sqrt(x) = 4 - 5 = -1\r<BR>\n" );
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document.write( "when you shift it to the right by 3 units, the check points become x = 11 and x = 35.<BR>\n" );
document.write( "when x = 11, sqrt(x) = -3.<BR>\n" );
document.write( "when x = 35, sqrt(x) = -1.\r<BR>\n" );
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