move the slider on the graph on the right to graph each function and describe the translation.\nfunction…

Explanation:

Step1: Recall translation rules

For a function $y = f(x - h)+k$, $h$ represents horizontal translation and $k$ represents vertical translation. If $h>0$, shift right; if $h < 0$, shift left. If $k>0$, shift up; if $k < 0$, shift down. The parent - function is $y=\sqrt{x}$.

Step2: Analyze $y=\sqrt{x + 4}$

Rewrite it as $y=\sqrt{x-(-4)}+0$. Here $h=-4$ and $k = 0$. So it is a horizontal shift 4 units to the left.

Step3: Analyze $y=\sqrt{x - 4}$

Rewrite it as $y=\sqrt{x - 4}+0$. Here $h = 4$ and $k=0$. So it is a horizontal shift 4 units to the right.

Step4: Analyze $y=\sqrt{x}-2$

Rewrite it as $y=\sqrt{x-0}+(-2)$. Here $h = 0$ and $k=-2$. So it is a vertical shift 2 units down.

Step5: Analyze $y=\sqrt{x}+2$

Rewrite it as $y=\sqrt{x-0}+2$. Here $h = 0$ and $k = 2$. So it is a vertical shift 2 units up.

Answer:

$y=\sqrt{x + 4}$: 4 units left; $y=\sqrt{x - 4}$: 4 units right; $y=\sqrt{x}-2$: 2 units down; $y=\sqrt{x}+2$: 2 units up.