document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621329>Question 621329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Specify the sequence transformations that will yield the graph of the given function from the graph of the function f(x)= x^3\r<BR>\n" );
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document.write( "G(x)= -(x-4)^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390790 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5396)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How could we do that transformation? Let me count the ways.<BR>\n" );
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document.write( "The answer could be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > shift to the right by 4 units<BR>\n" );
document.write( "followed by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-%28x-4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=-%28x-4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > flip over the x-axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C%28x-4%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C%28x-4%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C-%28x-4%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C-%28x-4%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That's the first way that comes to mind, and simple minds would look no further.<BR>\n" );
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document.write( "You could flip first, and shift later, too.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > flip over the x-axis.<BR>\n" );
document.write( "followed by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-%28x-4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=-%28x-4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > shift to the right by 4 units.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C-x%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C-x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C-%28x-4%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C-%28x-4%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "because if you change x to -x you get the same result:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28-x%29%5E3=-x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=%28-x%29%5E3=-x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(Unless you are watching while the function is being flipped you would not know which way it was flipped).<BR>\n" );
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document.write( "You could also shift left to start, and then flip over the y-axis:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28-x%2B4%29%5E3=-%28x-4%29%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=%28-x%2B4%29%5E3=-%28x-4%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C%28x%2B4%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C%28x%2B4%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C%28-x%2B4%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C300%2C-8%2C8%2C-20%2C20%2C%28-x%2B4%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );