Question 1174661

Explain the transformation rules for graphing the given function y= -2 cuberoot(x-2) + 1
<pre>   <b><u>The parent function:</b></u> y = {{{root(3, x)}}}                               The function: y = {{{root(3, (x - 2))}}}
{{{graph( 300, 300, -4, 6, -4, 6, 
              grid(1),
              x^(1/3), -(-x)^(1/3))}}}             {{{graph( 300, 300, -4, 6, -4, 6, 
              grid(1),
              (x - 2)^(1/3), -(- x + 2)^(1/3))}}}</pre>
<pre>     The function: y = {{{root(3, (x - 2)) + 1}}}                          The function: y = {{{- root(3, (x - 2)) + 1)}}}
{{{graph( 300, 300, -4, 6, -4, 6, 
              grid(1),
              (x - 2)^(1/3) + 1, -(-x + 2)^(1/3) + 1)}}}              {{{graph( 300, 300, -4, 6, -4, 6, 
              grid(1),
              - (x - 2)^(1/3) + 1, (- x + 2)^(1/3) + 1)}}}</pre><pre>                                  The FINAL function: y = {{{- 2 * root(3, (x - 2)) + 1)}}}
                                 {{{graph( 300, 300, -4, 6, -4, 6, 
              grid(1),
              - 2(x - 2)^(1/3) + 1, 2(- x + 2)^(1/3) + 1)}}}
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Do you need any more explanations? I hope NOT!!</pre>