Question

move the slider on the graph on the right to graph each function and describe the translation. function position relative to parent ( y = sqrt{x + 4} ) left of the parent ( y = sqrt{x - 1} ) right of the parent ( y = sqrt{x - 2} ) below the parent ( y = sqrt{x + 2} ) above the parent complete ( y = sqrt{x - 3} + 2 ) ( y = sqrt{x + 3} - 2 ) done intro

Explanation:

Step1: Recall translation rules

For parent function $y=\sqrt{x}$, transformed function $y=\sqrt{x-h}+k$ has:

• Horizontal shift: $h>0$ right, $h<0$ left
• Vertical shift: $k>0$ up, $k<0$ down

Step2: Analyze $y=\sqrt{x-3}+2$

Here $h=3$, $k=2$. So shift right 3, up 2.
Position: right of parent, above the parent

Step3: Analyze $y=\sqrt{x+3}-2$

Rewrite as $y=\sqrt{x-(-3)}+(-2)$. Here $h=-3$, $k=-2$. So shift left 3, down 2.
Position: left of parent, below the parent

Answer:

Function	Position Relative to Parent
$y=\sqrt{x-4}$	right of the parent
$y=\sqrt{x}-2$	below the parent
$y=\sqrt{x}+2$	above the parent
$y=\sqrt{x-3}+2$	right of the parent, above the parent
$y=\sqrt{x+3}-2$	left of the parent, below the parent