Question

know the parent ca the graph on the right to graph each function and describe the transformation.
function
position relative to parent
( y = sqrt{x + 4} )
( y = sqrt{x - 4} )
( y = sqrt{x} - 2 )
( y = sqrt{x} + 2 )

(graph part with ( y = sqrt{x} ) (dashed) and another square - root graph (red), and sliders for ( h ) and ( k ))

Explanation:

Step1: Identify parent function

Parent function: $y=\sqrt{x}$

Step2: Match graph to transformed form

The transformed function form is $y=\sqrt{x-h}+k$. The red graph shifts left 4 units from $y=\sqrt{x}$, so $h=-4$, $k=0$. The function is $y=\sqrt{x+4}$.

Step3: Describe the translation

A left shift by 4 units means replacing $x$ with $x+4$ in the parent function.

Answer:

Function & Translation Match:

• $y=\sqrt{x+4}$: Translated 4 units left from $y=\sqrt{x}$
• $y=\sqrt{x-4}$: Translated 4 units right from $y=\sqrt{x}$
• $y=\sqrt{x}-2$: Translated 2 units down from $y=\sqrt{x}$
• $y=\sqrt{x}+2$: Translated 2 units up from $y=\sqrt{x}$

Graph in the image:

The red graph corresponds to $y=\sqrt{x+4}$, with translation: 4 units left relative to the parent function $y=\sqrt{x}$