document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177624>Question 1177624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe a series of transformations from the parent function, f(x) = x^n that gives us g(x)= 1/3(x+2)^3 -1. Be sure the transformations are written in the proper order.  </SPAN>\n" );
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document.write( "The 1/3 shrinks the graph vertically by a factor of 3 (i.e., \"stretches\" it by a factor of 1/3).<br><BR>\n" );
document.write( "The x+2 shifts the graph 2 units to the left.<br><BR>\n" );
document.write( "The -1 shifts the graph 1 unit down.<br><BR>\n" );
document.write( "The order of the transformations is the order in which you would apply the changes if you were evaluating the expression for a given value of x, using standard order of operations:<br><BR>\n" );
document.write( "first: simplify inside parentheses: x+2: shift left 2<BR>\n" );
document.write( "second: multiplication/division: 1/3: shrink vertically<BR>\n" );
document.write( "third: addition/subtraction: -1: shift down 1<br><BR>\n" );
document.write( "Parent function: x^3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "first transformation: (x+2)^3: shift left 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%2C%28x%2B2%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%2C%28x%2B2%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "second transformation: (1/3)(x+2)^3: shrink by a factor of 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%2C%28x%2B2%29%5E3%2C%281%2F3%29%28x%2B2%29%5E3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "third transformation: (1/3)(x+2)^3-1: shift down 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C3%2C-50%2C50%2Cx%5E3%2C%28x%2B2%29%5E3%2C%281%2F3%29%28x%2B2%29%5E3%2C%281%2F3%29%28x%2B2%29%5E3-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );