Question 1203062
Consider the function g(x) = -2(2) ^ ½(x+2) + 3.
What is the base (parent) function? 
<pre>
{{{p(x)=2^x}}} <--base (parent) function
{{{graph(400,400,-5,5,-2,8,2^x)}}}{{{matrix(6,2,x,y,-2,0.25,-1,0.5,0,1,1,2,2,4)}}}
{{{matrix(2,1,"",y=p(expr(1/2)x)=2^(expr(1/2)x))}}} <-- multiplying x by {{{1/2}}} stretches graph horizontally by a factor of {{{1^""/(1/2)=2}}}
{{{graph(400,400,-5,5,-2,8,2^(0.5x))}}}{{{matrix(6,2,x,y,-2,0.5,-1,0.707,0,1,1,1.414,2,2)}}}
{{{matrix(2,1,"",y=p(expr(1/2)(x-2))=2^(expr(1/2)(x+2))))}}} <-- adding 2 to x shifts graph left 2 units.
{{{graph(400,400,-5,5,-2,8,2^(0.5(x+2)))}}}{{{matrix(6,2,x,y,-2,1,-1,1.414,0,2,1,2.83,2,4)}}}
{{{matrix(2,1,"",y=2p(expr(1/2)(x-2))=2*2^(expr(1/2)(x+2)))}}} <-- multiplying entire right side by 2 stretches graph vertically by a factor of 2.
{{{graph(400,400,-5,5,-2,8,2*2^(0.5(x+2)))}}}{{{matrix(6,2,x,y,-2,2,-1,2.828,0,4,1,5.657,2,8)}}}
{{{matrix(2,1,"",y=-2p(expr(1/2)(x-2))=-2*2^(expr(1/2)(x+2)))}}} <-- multiplying the entire right side by -1 reflects graph across the x-axis.
{{{graph(400,400,-5,5,-8,2,-2*2^(0.5(x+2)))}}}{{{matrix(6,2,x,y,-2,-2,-1,-2.828,0,-4,1,-5.657,2,-8)}}}
{{{matrix(2,1,"","g(x)"=-2p(expr(1/2)(x-2))+3=-2*2^(expr(1/2)(x+2))+3)}}} <-- adding 3 to the entire right side shifts  graph upward 3 units.
{{{graph(400,400,-5,5,-8,2,-2*2^(0.5(x+2))+3)}}}{{{matrix(6,2,x,y,-2,1,-1,0.172,0,-1,1,-2.657,2,-5)}}}

The mapping rule from base (parent) function p(x) to g(x) is {{{"g(x)"=-2p(expr(1/2)(x-2))+3}}}

Edwin</pre>