Question 1200477
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<font color=red>Answer:</font> {{{y = sqrt(x+6)}}}



Explanation:
Imagine parent function square root curve {{{y = sqrt(x)}}} is etched in stone on the wall. 
As such, the curve itself cannot move.
Further, imagine that we can move the xy axis around like a target scope. 
Imagine the axis is part of the camera that moves around.
Moving the xy axis 6 units to the right gives the illusion the curve {{{y = sqrt(x)}}} moves 6 units to the left (even though the curve is still etched in stone).


Moving the xy axis 6 units to the right means each old input x is updated to the new input x+6


We go from {{{y = sqrt(x)}}} to {{{y = sqrt(x+6)}}} (replace each x with x+6)


Confirmation with a graph
{{{
graph(300,300,-8,5,-4,4,-100,sqrt(x),sqrt(x+6))
}}}
{{{y = sqrt(x)}}} in green
{{{y = sqrt(x+6)}}} in blue
Desmos and GeoGebra are two graphing options I recommend.


Plug x = -6 into {{{y = sqrt(x+6)}}} to find that:
{{{y = sqrt(x+6)}}}
{{{y = sqrt(-6+6)}}}
{{{y = sqrt(0)}}}
{{{y = 0}}}
Therefore, (-6,0) is on the curve {{{y = sqrt(x+6)}}}
This is indicated as the left-most point of the blue curve shown above.
I'll let you try other x values.
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