document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200477>Question 1200477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph.\r<BR>\n" );
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document.write( "f(x)= √x ; shift 6 units to the left\r<BR>\n" );
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document.write( "y= (blank)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834616 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<font color=red>Answer:</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Explanation:<BR>\n" );
document.write( "Imagine parent function square root curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is etched in stone on the wall. <BR>\n" );
document.write( "As such, the curve itself cannot move.<BR>\n" );
document.write( "Further, imagine that we can move the xy axis around like a target scope. <BR>\n" );
document.write( "Imagine the axis is part of the camera that moves around.<BR>\n" );
document.write( "Moving the xy axis 6 units to the right gives the illusion the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > moves 6 units to the left (even though the curve is still etched in stone).\r<BR>\n" );
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document.write( "Moving the xy axis 6 units to the right means each old input x is updated to the new input x+6\r<BR>\n" );
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document.write( "We go from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (replace each x with x+6)\r<BR>\n" );
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document.write( "Confirmation with a graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Agraph%28300%2C300%2C-8%2C5%2C-4%2C4%2C-100%2Csqrt%28x%29%2Csqrt%28x%2B6%29%29%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Agraph%28300%2C300%2C-8%2C5%2C-4%2C4%2C-100%2Csqrt%28x%29%2Csqrt%28x%2B6%29%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in green<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in blue<BR>\n" );
document.write( "Desmos and GeoGebra are two graphing options I recommend.\r<BR>\n" );
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document.write( "Plug x = -6 into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28-6%2B6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28-6%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%280%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore, (-6,0) is on the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%2B6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is indicated as the left-most point of the blue curve shown above.<BR>\n" );
document.write( "I'll let you try other x values.<BR>\n" );
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