Lesson HOW TO PLOT transformed functions

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<H2>HOW TO PLOT transformed functions</H2>

<H3>Problem 1</H3>Explain the transformation rules for graphing the given function  &nbsp;&nbsp;y = -{{{2*root(3,x-2) + 1}}}

<B>Solution</B>

<pre>
The function  y = {{{-2*root(3,(x-2)) +1}}}  is the "child" function of the "parent" function  y= {{{root(3,x)}}}.

The parent function is defined over the ENTIRE real domain (whole number line), see the plot in Figure 1.

{{{graph( 300, 300, -4, 6, -4, 6, 
              grid(1),
              x^(1/3), -(-x)^(1/3)

)}}}

Figure 1.  y = {{{root(3,x)}}}

The plot has two wings (two branches), the green line (at x >=0) and the blue line (at x < 0).

They both have EQUAL RIGHTS of existence and are antisymmetric relatively the origin of the coordinate system.

The "child" function  y= {{{-2*root(3,(x-2)) +1}}}  is ALSO defined over the ENTIRE number line.

Relative to the parent function plot, it is shifted two units right, stretched two times along the y-axis 
and reflected relative the x-axis; then shifted 1 unit up.

See the Figure 2.

{{{graph( 300, 300, -4, 6, -4, 6, 
              grid(1),
              -2(x-2)^(1/3)+1, 2(-(x-2))^(1/3)+1

)}}}

Figure 2.  y = {{{-2*root(3,(x-2))+1}}}

</pre>